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 Extending Modules written by Nguyen Viet Dung and published by Routledge. This book was released on 2019-01-22 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its
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 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 124 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 On Quotient Rings and M injective Modules written by Karen L. Kruschwitz and published by . This book was released on 1972 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our main purpose in this paper is to show that the integers can be embedded in a field of equivalence classes of linear mappings and to extend this to arbitrary rings. We will then generalize our results to modules.
Download or read book Injective Modules and Injective Quotient Rings written by Carl Faith and published by . This book was released on 2020-12-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Injective Modules and Injective Quotient Rings, in two parts, is the only book of its kind to combine commutative and noncommutative ring theory. This unique and outstanding contribution to the mathematical literature will immediately advance the studies of mathematicians and graduate students in the field. Written by a leading expert in the field, Injective Modules and Injective Quotient Rings offers readers the key concepts and methods used in both noncommutative and commutative ring theory. Part I provides the first non-torsion-theory proof of the Teply-Miller theorem and the first statement and proof of the converse of the Teply-Miller-Hansen theorem. Many applications of these theorems to the structure of rings and modules are given, including generalizations of theorems of Cailleau-Beck and Matlis on the structure of ∑-injectives and commutative rings. Part II provides an alternative approach to the solution of Kaplansky's problem on the classification of FGC rings. Of particular importance is the consistent use of noncommutative ring theoretical techniques throughout Part II to obtain theorems lying purely in the domain of commutative ring theory. Graduate students and mathematicians in both commutative and noncommutative ring theory will learn from the unique approach and new general methods in ring theory contained in Injective Modules and Injective Quotient Rings.
Download or read book Semidistributive Modules and Rings written by A.A. Tuganbaev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive.
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 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 Quotient Rings written by Hildigunnur Halldórsdóttir and published by . This book was released on 1967 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rings Modules and the Total written by Friedrich Kasch and published by Springer Science & Business Media. This book was released on 2004-06-25 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to anyone with a basic knowledge of ring and module theory A short introduction to torsion-free Abelian groups is included
Download or read book Report on Injective Modules written by Chi-te Tsai and published by Kingston, Ont : Queen's University, 1965 [c1966]. This book was released on 1965 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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 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.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1963 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
