Introduction To Ring Theory PDF Download
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Author | : Paul M. Cohn |
Publisher | : Springer Science & Business Media |
Total Pages | : 234 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1447104757 |
Download Introduction to Ring Theory Book in PDF, ePub and Kindle
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 | : A. J. Berrick |
Publisher | : Cambridge University Press |
Total Pages | : 286 |
Release | : 2000-05 |
Genre | : Mathematics |
ISBN | : 9780521632744 |
Download An Introduction to Rings and Modules Book in PDF, ePub and Kindle
This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.
Author | : B. Stenström |
Publisher | : Springer Science & Business Media |
Total Pages | : 319 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642660665 |
Download Rings of Quotients Book in PDF, ePub and Kindle
The theory of rings of quotients has its origin in the work of (j). Ore and K. Asano on the construction of the total ring of fractions, in the 1930's and 40's. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R. E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A. It may be characterized by the two properties: (i) For every qEQ there exists a non-zero SEA such that qSEA. (ii) Q is the maximal over-ring of A satisfying condition (i). The well-known construction of Q can be immediately extended to the case when A is an arbitrary commutative ring and S is a multiplicatively closed set of non-zero-divisors of A. In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb. The resulting ring Q satisfies (i), with the extra requirement that SES, and (ii).
Author | : Ken Levasseur |
Publisher | : Lulu.com |
Total Pages | : 574 |
Release | : 2012-02-25 |
Genre | : Applied mathematics |
ISBN | : 1105559297 |
Download Applied Discrete Structures Book in PDF, ePub and Kindle
Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
Author | : Donald S. Passman |
Publisher | : American Mathematical Soc. |
Total Pages | : 324 |
Release | : 2004-09-28 |
Genre | : Mathematics |
ISBN | : 9780821869383 |
Download A Course in Ring Theory Book in PDF, ePub and Kindle
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 | : Hideyuki Matsumura |
Publisher | : Cambridge University Press |
Total Pages | : 338 |
Release | : 1989-05-25 |
Genre | : Mathematics |
ISBN | : 9780521367646 |
Download Commutative Ring Theory Book in PDF, ePub and Kindle
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author | : C. Nastasescu |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 1987-04-30 |
Genre | : Mathematics |
ISBN | : 9789027724618 |
Download Dimensions of Ring Theory Book in PDF, ePub and Kindle
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author | : Robert Wisbauer |
Publisher | : Routledge |
Total Pages | : 425 |
Release | : 2018-05-11 |
Genre | : Mathematics |
ISBN | : 1351447343 |
Download Foundations of Module and Ring Theory Book in PDF, ePub and Kindle
This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Author | : R. B. J. T. Allenby |
Publisher | : Butterworth-Heinemann |
Total Pages | : 383 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 9780340544402 |
Download Rings, Fields and Groups Book in PDF, ePub and Kindle
Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses
Author | : T.Y. Lam |
Publisher | : Springer Science & Business Media |
Total Pages | : 410 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468404067 |
Download A First Course in Noncommutative Rings Book in PDF, ePub and Kindle
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.