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Author : David M. Burton
Publisher : Addison-Wesley
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.3/5 (91 download)
Download or read book A First Course in Rings and Ideals written by David M. Burton and published by Addison-Wesley. This book was released on 1970 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : T.Y. Lam
Publisher : Springer Science & Business Media
ISBN 13 : 1468404067
Total Pages : 410 pages
Book Rating : 4.4/5 (684 download)
Download or read book A First Course in Noncommutative Rings written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan dard first-year graduate course in abstract algebra.
Author : Marlow Anderson
Publisher : CRC Press
ISBN 13 : 1420057111
Total Pages : 684 pages
Book Rating : 4.4/5 (2 download)
Download or read book A First Course in Abstract Algebra written by Marlow Anderson and published by CRC Press. This book was released on 2005-01-27 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
Author : Shahriar Shahriar
Publisher : American Mathematical Soc.
ISBN 13 : 1470428490
Total Pages : 675 pages
Book Rating : 4.4/5 (74 download)
Download or read book Algebra in Action: A Course in Groups, Rings, and Fields written by Shahriar Shahriar and published by American Mathematical Soc.. This book was released on 2017-08-16 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Author : Donald S. Passman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821869383
Total Pages : 324 pages
Book Rating : 4.8/5 (693 download)
Download or read book A Course in Ring Theory written by Donald S. Passman and published by American Mathematical Soc.. This book was released on 2004-09-28 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderburn rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index
Author : Nathan Jacobson
Publisher : American Mathematical Soc.
ISBN 13 : 0821815024
Total Pages : 150 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Theory of Rings written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1943-12-31 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
Author : Joseph J. Rotman
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.F/5 ( download)
Download or read book A First Course in Abstract Algebra written by Joseph J. Rotman and published by . This book was released on 2000 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: For one-semester or two-semester undergraduate courses in Abstract Algebra. This new edition has been completely rewritten. The four chapters from the first edition are expanded, from 257 pages in first edition to 384 in the second. Two new chapters have been added: the first 3 chapters are a text for a one-semester course; the last 3 chapters are a text for a second semester. The new Chapter 5, Groups II, contains the fundamental theorem of finite abelian groups, the Sylow theorems, the Jordan-Holder theorem and solvable groups, and presentations of groups (including a careful construction of free groups). The new Chapter 6, Commutative Rings II, introduces prime and maximal ideals, unique factorization in polynomial rings in several variables, noetherian rings and the Hilbert basis theorem, affine varieties (including a proof of Hilbert's Nullstellensatz over the complex numbers and irreducible components), and Grobner bases, including the generalized division algorithm and Buchberger's algorithm.
Author : Tsit-Yuen Lam
Publisher : Springer Science & Business Media
ISBN 13 : 1441986162
Total Pages : 406 pages
Book Rating : 4.4/5 (419 download)
Download or read book A First Course in Noncommutative Rings written by Tsit-Yuen Lam and published by Springer Science & Business Media. This book was released on 2013-01-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.
Author : Craig Huneke
Publisher : Cambridge University Press
ISBN 13 : 0521688604
Total Pages : 446 pages
Book Rating : 4.5/5 (216 download)
Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author : T.Y. Lam
Publisher : Springer Science & Business Media
ISBN 13 : 0387488995
Total Pages : 427 pages
Book Rating : 4.3/5 (874 download)
Download or read book Exercises in Modules and Rings written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2009-12-08 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Author : Paul M. Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 1447104757
Total Pages : 234 pages
Book Rating : 4.4/5 (471 download)
Download or read book Introduction to Ring Theory written by Paul M. Cohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
Author : Daniel G. Coronell
Publisher : CRC Press
ISBN 13 : 1584885157
Total Pages : 693 pages
Book Rating : 4.5/5 (848 download)
Download or read book Introduction to MATLAB with Applications for Chemical and Mechanical Engineers written by Daniel G. Coronell and published by CRC Press. This book was released on 2015-10-15 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to MATLAB with Applications for Chemical and Mechanical Engineers provides applications from chemical engineering and biotechnology, such as thermodynamics, heat transfer, fluid mechanics, and mass transfer. The book features a section on input, output, and storage of data as well as a section on data analysis and parameter estimation that contains statistical analysis, curve fitting optimization, and error analysis. Many applied case studies are included from the engineering disciplines. It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.
Author : David A.R. Wallace
Publisher : Springer Science & Business Media
ISBN 13 : 1447104250
Total Pages : 256 pages
Book Rating : 4.4/5 (471 download)
Download or read book Groups, Rings and Fields written by David A.R. Wallace and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.
Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
ISBN 13 : 0821847996
Total Pages : 516 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebra written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2009 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: as a student." --Book Jacket.
Author : Paolo Aluffi
Publisher : American Mathematical Soc.
ISBN 13 : 147046571X
Total Pages : 713 pages
Book Rating : 4.4/5 (74 download)
Download or read book Algebra: Chapter 0 written by Paolo Aluffi and published by American Mathematical Soc.. This book was released on 2021-11-09 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author : Stephen Lovett
Publisher : CRC Press
ISBN 13 : 1000605442
Total Pages : 570 pages
Book Rating : 4.0/5 (6 download)
Download or read book Abstract Algebra written by Stephen Lovett and published by CRC Press. This book was released on 2022-07-05 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?" Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, −, ×, and ÷) on real numbers. Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties. This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory. The writing style is student-centered, conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography and many other areas. This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation. The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and to trying to answer their own questions. Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician’s work through responsible research. The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field.
Author : Mike E Keating
Publisher : World Scientific
ISBN 13 : 1783262400
Total Pages : 271 pages
Book Rating : 4.7/5 (832 download)
Download or read book A First Course In Module Theory written by Mike E Keating and published by World Scientific. This book was released on 1998-07-31 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to module theory for the reader who knows something about linear algebra and ring theory. Its main aim is the derivation of the structure theory of modules over Euclidean domains. This theory is applied to obtain the structure of abelian groups and the rational canonical and Jordan normal forms of matrices. The basic facts about rings and modules are given in full generality, so that some further topics can be discussed, including projective modules and the connection between modules and representations of groups.The book is intended to serve as supplementary reading for the third or fourth year undergraduate who is taking a course in module theory. The further topics point the way to some projects that might be attempted in conjunction with a taught course.
