Download or read book Algebra II Ring Theory written by Carl Faith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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 160 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.

Download or read book Undergraduate Algebra written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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

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

Download or read book Algebra Ii Ring Theory written by Carl Faith and published by . This book was released on 1976 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Download or read book Rings of Quotients written by B. Stenström and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Download or read book Abstract Algebra written by Thomas Judson and published by Orthogonal Publishing L3c. This book was released on 2023-08-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Algebra II written by N. Bourbaki and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki’s Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.

Download or read book Undergraduate Commutative Algebra written by Miles Reid and published by Cambridge University Press. This book was released on 1995-11-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.

Download or read book Ring Theory And Algebraic Geometry written by A. Granja and published by CRC Press. This book was released on 2001-05-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses 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.

Download or read book Counterexamples in Topology written by Lynn Arthur Steen and published by Courier Corporation. This book was released on 2013-04-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

Download or read book Abstract Algebra with Applications written by Karlheinz Spindler and published by CRC Press. This book was released on 2018-05-04 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Download or read book Basic Algebra I written by Nathan Jacobson and published by Courier Corporation. This book was released on 2009-06-22 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Explores all of the topics typically covered in undergraduate courses including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra"--Cover p. 4

Download or read book Algebra II Ring Theory written by Carl Faith and published by . This book was released on 1976-09-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: