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Author : Francis Sowerby Macaulay
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by . This book was released on 1916 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : F S Macaulay
Publisher : Legare Street Press
ISBN 13 : 9781021186263
Total Pages : 0 pages
Book Rating : 4.1/5 (862 download)
Download or read book The Algebraic Theory of Modular Systems written by F S Macaulay and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work by Francis S. Macaulay is a comprehensive exploration of the algebraic theory of modular systems. The book covers a range of topics, including the theory of groups, rings, fields, and modules, and provides a detailed analysis of the properties of modular systems. It is an essential resource for anyone interested in abstract algebra or mathematics in general. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : F S Macaulay
Publisher : Independently Published
ISBN 13 : 9781076727176
Total Pages : 148 pages
Book Rating : 4.7/5 (271 download)
Download or read book The Algebraic Theory of Module Systems written by F S Macaulay and published by Independently Published. This book was released on 2019-06-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE present state of our knowledge of the properties of Modular Systems is chiefly due to the fundamental theorems and processes of L. Kronecker, M. Noether, D. Hilbert, and E. Lasker, and above all to J. Konig's profound exposition and numerous extensions of Kronecker's theory (p. xiii). Konig's treatise might be regarded as in some measure complete if it were admitted that a problem is finished with when its solution has been reduced to a finite number of feasible operations. If however the operations are too numerous or too involved to be carried out in practice the solution is only a theoretical one; and its importance then lies not in itself, but in the theorems with which it is associated and to which it leads. Such a theoretical solution must be regarded as a preliminary and not the final stage in the consideration of the problem. In the following presentment of the subject Section I is devoted to the Resultant, the case of equations being treated in a parallel manner to that of two equations; Section II contains an account of Kronecker's theory of the Resolvent, following mainly the lines of Konig's exposition; Section III, on general properties, is closely allied to Lasker's memoir and Dedekind's theory of Ideals; and Section IV is an extension of Lasker's results founded on the methods originated by Noether. The additions to the theory consist of one or two isolated theorems (especially §§ 50 - 53 and § 79 and its consequences) and the introduction of the Inverse System in Section IV. The subject is full of pitfalls. I have pointed out some mistakes made by others, but have no doubt that I have made new ones. It may be expected that any errors will be discovered and eliminated in due course, since proofs or references are given for all major and most minor statements. I take this opportunity of thanking the Editors for their acceptance of this tract and the Syndics of the University Press for publishing it.
Author : William A. Adkins
Publisher : Springer Science & Business Media
ISBN 13 : 1461209234
Total Pages : 540 pages
Book Rating : 4.4/5 (612 download)
Download or read book Algebra written by William A. Adkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.
Author : Francis Sowerby Macaulay
Publisher : Palala Press
ISBN 13 : 9781359668806
Total Pages : pages
Book Rating : 4.6/5 (688 download)
Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by Palala Press. This book was released on 2016-05-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : FRANCIS SOWERBY. MACAULAY
Publisher :
ISBN 13 : 9781033349946
Total Pages : 0 pages
Book Rating : 4.3/5 (499 download)
Download or read book ALGEBRAIC THEORY OF MODULAR SYSTEMS written by FRANCIS SOWERBY. MACAULAY and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Francis Sowerby Macaulay
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (89 download)
Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by . This book was released on 1916 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Francis Sowerby Macaulay
Publisher : Forgotten Books
ISBN 13 : 9781330386675
Total Pages : 133 pages
Book Rating : 4.3/5 (866 download)
Download or read book The Algebraic Theory of Modular Systems written by Francis Sowerby Macaulay and published by Forgotten Books. This book was released on 2015-06-25 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Algebraic Theory of Modular Systems The present state of our knowledge of the properties of Modular Systems is chiefly due to the fundamental theorems and processes of L. Kronecker, M. Noether, D. Hilbert, and E. Lasker, and above all to J. Konig's profound exposition and numerous extensions of Kronecker's theory (p. xiii). Konig's treatise might be regarded as in some measure complete if it were admitted that a problem is finished with when its solution has been reduced to a finite number of feasible operations. If however the operations are too numerous or too involved to be carried out in practice the solution is only a theoretical one; and its importance then lies not in itself, but in the theorems with which it is associated and to which it leads. Such a theoretical solution must be regarded as a preliminary and not the final stage in the consideration of the problem. In the following presentment of the subject Section I is devoted to the Resultant, the case of n equations being treated in a parallel manner to that of two equations; Section II contains an account of Kronecker's theory of the Resolvent, following mainly the lines of Konig's exposition; Section III, on general properties, is closely allied to Lasker's memoir and Dedekind's theory of Ideals; and Section IV is an extension of Lasker's results founded on the methods originated by Noether. The additions to the theory consist of one or two isolated theorems (especially 50-53 and 79 and its consequences) and the introduction of the Inverse System in Section IV. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : F. Macaulay
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781976536939
Total Pages : 148 pages
Book Rating : 4.5/5 (369 download)
Download or read book The Algebraic Theory of Modular Systems written by F. Macaulay and published by Createspace Independent Publishing Platform. This book was released on 2017-09-18 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface. THE present state of our knowledge of the properties of Modular Systems is chiefly due to the fundamental theorems and processes of L. Kronecker, M. Noether, D. Hilbert, and E. Lasker, and above all to J. Konig's profound exposition and numerous extensions of Kronecker's theory (p. xiii). Konig's treatise might be regarded as in some measure complete if it were admitted that a problem is finished with when its solution has been reduced to a finite number of feasible operations. If however the operations are too numerous or too involved to be carried out in practice the solution is only a theoretical one; and its importance then lies not in itself, but in the theorems with which it is associated and to which it leads. Such a theoretical solution must be regarded as a preliminary and not the final stage in the consideration of the problem. In the following presentment of the subject Section I is devoted to the Resultant, the case of equations being treated in a parallel manner to that of two equations; Section II contains an account of Kronecker's theory of the Resolvent, following mainly the lines of Konig's exposition ; Section III, on general properties, is closely allied to Lasker's memoir and Dedekind's theory of Ideals; and Section IV is an extension of Lasker's results founded on the methods originated by Noether. The additions to the theory consist of one or two isolated theorems (especially §§ 50 - 53 and § 79 and its consequences) and the introduction of the Inverse System in Section IV. The subject is full of pitfalls. I have pointed out some mistakes made by others, but have no doubt that I have made new ones. It may be expected that any errors will be discovered and eliminated in due course, since proofs or references are given for all major and most minor statements. I take this opportunity of thanking the Editors for their acceptance of this tract and the Syndics of the University Press for publishing it.
Author : John Dauns
Publisher : Cambridge University Press
ISBN 13 : 0521462584
Total Pages : 470 pages
Book Rating : 4.5/5 (214 download)
Download or read book Modules and Rings written by John Dauns and published by Cambridge University Press. This book was released on 1994-10-28 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
Author : Joachim Lambek
Publisher : American Mathematical Soc.
ISBN 13 : 082184900X
Total Pages : 196 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Rings and Modules written by Joachim Lambek and published by American Mathematical Soc.. This book was released on 2009 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces.Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course]...in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need.In addition to covering the basic topics...the author covers some topics not so readily available to the nonspecialist...the chapters are written to be as independent as possible...[which will be appreciated by] students making their first acquaintance with the subject...one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H)
Author : William A. Adkins
Publisher : Springer Science & Business Media
ISBN 13 : 9780387978390
Total Pages : 548 pages
Book Rating : 4.9/5 (783 download)
Download or read book Algebra written by William A. Adkins and published by Springer Science & Business Media. This book was released on 1992 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: First year graduate algebra text. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in group and ring theory, the authors then develop basic module theory and its use in investigating bilinear, sesquilinear, and quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Ryoshi Hotta
Publisher : Springer Science & Business Media
ISBN 13 : 081764363X
Total Pages : 408 pages
Book Rating : 4.8/5 (176 download)
Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
Author : Golan
Publisher : CRC Press
ISBN 13 : 1351430378
Total Pages : 272 pages
Book Rating : 4.3/5 (514 download)
Download or read book Modules and the Structure of Rings written by Golan and published by CRC Press. This book was released on 2017-10-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : 382 pages
Book Rating : 4.4/5 (91 download)
Download or read book Algebraic D-modules written by Armand Borel and published by . This book was released on 1987 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.
Author : Athanasios C. Antoulas
Publisher : Springer Science & Business Media
ISBN 13 : 3662085461
Total Pages : 589 pages
Book Rating : 4.6/5 (62 download)
Download or read book Mathematical System Theory written by Athanasios C. Antoulas and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.
Author : André Leroy
Publisher : American Mathematical Soc.
ISBN 13 : 1470441047
Total Pages : 355 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rings, Modules and Codes written by André Leroy and published by American Mathematical Soc.. This book was released on 2019-04-12 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.
