Download or read book Rings of Quotients and Quotient Modules written by Cathleen Clare Real and published by . This book was released on 1968 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Injective Modules and Injective Quotient Rings written by Carl Faith and published by CRC Press. This book was released on 2019-08-21 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)
Download or read book Lectures on Injective Modules and Quotient Rings written by Carl Faith and published by Springer. This book was released on 2006-11-14 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Rings and Modules of Quotients written by B. Stenström and published by Lecture Notes in Mathematics. This book was released on 1971 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modules of Quotients and Classical Quotient Rings written by Daniel C. Sims and published by . This book was released on 1972 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our overall purpose in this thesis will be to extend Ore's Condition to modules and then to apply those conditions to rings.
Download or read book Rings and Modules of Quotients written by B. Stenström and published by Springer. This book was released on 2006-11-15 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Injective Modules and Quotient Rings written by Carl Clifton Faith and published by . This book was released on 1967 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modules and Rings written by John Dauns and published by Cambridge University Press. This book was released on 1994-10-28 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.
Download or read book INJECTIVE MODULES AND INJECTIVE QUOTIENT RINGS written by Carl Faith and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E, R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e. all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)
Download or read book Extensions of Rings and Modules written by Gary F. Birkenmeier and published by Springer Science & Business Media. This book was released on 2013-07-19 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull). Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.
Download or read book Rings and Modules of Quotients written by B. Stenstrom and published by . This book was released on 2014-09-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Rings and Modules written by Joachim Lambek and published by American Mathematical Soc.. This book was released on 2009 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a particular emphasis on the concept of the complete ring of quotients. A survey of the fundamental concepts of algebras in the first chapter helps to make the treatment self-contained. The topics covered include selected results on Boolean and other commutative rings, the classical structure theory of associative rings, injective modules, and rings of quotients. The final chapter provides an introduction to homological algebra. Besides three appendices on further results, there is a six-page section of historical comments. Table of Contents: Fundamental Concepts of Algebra: 1.1 Rings and related algebraic systems; 1.2 Subrings, homomorphisms, ideals; 1.3 Modules, direct products, and direct sums; 1.4 Classical isomorphism theorems. Selected Topics on Commutative Rings: 2.1 Prime ideals in commutative rings; 2.2 Prime ideals in special commutative rings; 2.3 The complete ring of quotients of a commutative ring; 2.4 Rings of quotients of commutative semiprime rings; 2.5 Prime ideal spaces.Classical Theory of Associative Rings: 3.1 Primitive rings; 3.2 Radicals; 3.3 Completely reducible modules; 3.4 Completely reducible rings; 3.5 Artinian and Noetherian rings; 3.6 On lifting idempotents; 3.7 Local and semiperfect rings. Injectivity and Related Concepts: 4.1 Projective modules; 4.2 Injective modules; 4.3 The complete ring of quotients; 4.4 Rings of endomorphisms of injective modules; 4.5 Regular rings of quotients; 4.6 Classical rings of quotients; 4.7 The Faith-Utumi theorem. Introduction to Homological Algebra: 5.1 Tensor products of modules; 5.2 Hom and $\otimes$ as functors; 5.3 Exact sequences; 5.4 Flat modules; 5.5 Torsion and extension products. Appendixes; Comments; Bibliography; Index. Review from Zentralblatt Math: Due to their clarity and intelligible presentation, these lectures on rings and modules are a particularly successful introduction to the surrounding circle of ideas. Review from American Mathematical Monthly: An introduction to associative rings and modules which requires of the reader only the mathematical maturity which one would attain in a first-year graduate algebra [course]...in order to make the contents of the book as accessible as possible, the author develops all the fundamentals he will need.In addition to covering the basic topics...the author covers some topics not so readily available to the nonspecialist...the chapters are written to be as independent as possible...[which will be appreciated by] students making their first acquaintance with the subject...one of the most successful features of the book is that it can be read by graduate students with little or no help from a specialist. (CHEL/283.H)
Download or read book Complexe cotangent et d formations written by and published by . This book was released on 1971 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quotient Rings and Embeddings of Noetherian Rings written by Anders Jensen and published by . This book was released on 1991 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semidistributive Modules and Rings written by Askar A. Tuganbaev and published by Springer Science & Business Media. This book was released on 1998 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces structural and homological methods of ring theory, and explains the relationship between semidistributive modules and flat, projective, injective, multiplication, and Bezout modules. Contains chapters on areas such as radicals and semisimple modules, rings of quotients, flat modules and semiperfect rings, semiheridity and invariant rings, endomorphism rings, skew-injective rings, and monoid rings. Includes chapter exercises. Background to the material can be found in most graduate level texts in algebra. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Modules and the Structure of Rings written by Golan and published by CRC Press. This book was released on 2017-10-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
