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Algebraic Theory Of Modular Systems
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Book Synopsis The Algebraic Theory of Modular Systems by : Francis Sowerby Macaulay
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:
Book Synopsis The Algebraic Theory of Modular Systems by : F S Macaulay
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.
Book Synopsis ALGEBRAIC THEORY OF MODULAR SYSTEMS by : FRANCIS SOWERBY. MACAULAY
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:
Book Synopsis The Algebraic Theory of Modular Systems by : Francis Sowerby Macaulay
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.
Book Synopsis The Algebraic Theory of Modular Systems by : Francis Sowerby Macaulay
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 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Algebraic Theory of Modular Systems by : F. Macaulay
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.
Book Synopsis The Algebraic Theory of Modular Systems by : Francis Sowerby Macaulay
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:
Book Synopsis The Algebraic Theory of Module Systems by : F S Macaulay
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.
Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1907 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bulletin (new Series) of the American Mathematical Society by :
Download or read book Bulletin (new Series) of the American Mathematical Society written by and published by . This book was released on 1907 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving by : Teo Mora
Download or read book Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving written by Teo Mora and published by Cambridge University Press. This book was released on 2015-08-07 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Book Synopsis Commutative Algebra by : David Eisenbud
Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 1995-03-30 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Book Synopsis Algebraic Theory of Processes by : Matthew Hennessy
Download or read book Algebraic Theory of Processes written by Matthew Hennessy and published by MIT Press (MA). This book was released on 1988 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Theory of Processes provides the first general and systematic introduction to the semantics of concurrent systems, a relatively new research area in computer science.
Book Synopsis Elementary and Analytic Theory of Algebraic Numbers by : Wladyslaw Narkiewicz
Download or read book Elementary and Analytic Theory of Algebraic Numbers written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Book Synopsis Computer Algebra Methods for Equivariant Dynamical Systems by : Karin Gatermann
Download or read book Computer Algebra Methods for Equivariant Dynamical Systems written by Karin Gatermann and published by Springer. This book was released on 2007-05-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Book Synopsis Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by : Kenji Iohara
Download or read book Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers written by Kenji Iohara and published by Springer Nature. This book was released on 2020-02-20 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.
Book Synopsis Library of Congress Subject Headings by : Library of Congress. Subject Cataloging Division
Download or read book Library of Congress Subject Headings written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1980 with total page 1314 pages. Available in PDF, EPUB and Kindle. Book excerpt: