Algebra II Ring Theory
Author: Carl Faith
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 319
ISBN-13: 3642653219
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Introduction to Ring Theory
Author: Paul M. Cohn
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 234
ISBN-13: 1447104757
DOWNLOAD EBOOKA 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.
Undergraduate Algebra
Author: Serge Lang
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 380
ISBN-13: 1475768982
DOWNLOAD EBOOKThe companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
The Theory of Rings
Author: Nathan Jacobson
Publisher: American Mathematical Soc.
Published: 1943-12-31
Total Pages: 160
ISBN-13: 0821815024
DOWNLOAD EBOOKThe 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.
A Course in Ring Theory
Author: Donald S. Passman
Publisher: American Mathematical Soc.
Published: 2004-09-28
Total Pages: 324
ISBN-13: 9780821869383
DOWNLOAD EBOOKProjective 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
A First Course in Abstract Algebra
Author: Marlow Anderson
Publisher: CRC Press
Published: 2005-01-27
Total Pages: 684
ISBN-13: 1420057111
DOWNLOAD EBOOKMost 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
Algebra Ii. Ring Theory
Author: Carl Faith
Publisher:
Published: 1976
Total Pages: 302
ISBN-13:
DOWNLOAD EBOOKFoundations of Module and Ring Theory
Author: Robert Wisbauer
Publisher: Routledge
Published: 2018-05-11
Total Pages: 622
ISBN-13: 1351447343
DOWNLOAD EBOOKThis 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.
Ring Theory And Algebraic Geometry
Author: A. Granja
Publisher: CRC Press
Published: 2001-05-08
Total Pages: 366
ISBN-13: 9780203907962
DOWNLOAD EBOOKFocuses on the interaction between algebra and algebraic geometry, including high-level research papers and surveys contributed by over 40 top specialists representing more than 15 countries worldwide. Describes abelian groups and lattices, algebras and binomial ideals, cones and fans, affine and projective algebraic varieties, simplicial and cellular complexes, polytopes, and arithmetics.
Rings of Quotients
Author: B. Stenström
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 319
ISBN-13: 3642660665
DOWNLOAD EBOOKThe 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).
