Download or read book Cyclic Modules and the Structure of Rings written by S.K. Jain and published by Oxford University Press. This book was released on 2012-09-27 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.
Download or read book Modules and the Structure of Rings written by Golan and published by CRC Press. This book was released on 1991-04-24 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers vital background information on methods for solving hard classification problems of algebraic structures. It explains how algebraists deal with the problem of the structure of modules over rings and how they make use of these structures to classify rings.
Download or read book Modules and the Structure of Rings written by Golan and published by Routledge. This book was released on 2017-10-19 with total page 193 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.
Download or read book Structure of Rings written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1956-12-31 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modules written by Thomas J. Head and published by . This book was released on 1974 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 425 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 A First Course In Module Theory written by Mike E Keating and published by World Scientific. This book was released on 1998-07-31 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to module theory for the reader who knows something about linear algebra and ring theory. Its main aim is the derivation of the structure theory of modules over Euclidean domains. This theory is applied to obtain the structure of abelian groups and the rational canonical and Jordan normal forms of matrices. The basic facts about rings and modules are given in full generality, so that some further topics can be discussed, including projective modules and the connection between modules and representations of groups.The book is intended to serve as supplementary reading for the third or fourth year undergraduate who is taking a course in module theory. The further topics point the way to some projects that might be attempted in conjunction with a taught course.
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 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 Modules and Rings written by David Alexander Ross Wallace and published by . This book was released on 1982 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rings and Their Modules written by Paul E. Bland and published by Walter de Gruyter. This book was released on 2011-02-01 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. The theme of the text is the interplay between rings and modules. At times rings are investigated by considering given sets of conditions on the modules they admit and at other times rings of a certain type are considered to see what structure is forced on their modules. Standard topics in ring and module theory such as chain conditions on rings and modules, injective and projective modules and semisimple rings are included as well as subjects like category theory and homological algebra. The text also contains presentations on topics such as flat modules and coherent rings, injective envelopes, projective covers and perfect rings, reflexive modules and quasi-Frobenius rings, and graded rings and modules. The book is a self-contained volume written in a very systematic style: all proofs are clear and easy for the reader to understand and all arguments are based on materials contained in the book. A problem sets follow each section. It is assumed that the reader is familiar with concepts such as Zorn's lemma, commutative diagrams and ordinal and cardinal numbers. It is also assumed that the reader has a basic knowledge of rings and their homomorphisms. The text is suitable for graduate and PhD students who have chosen ring theory for their research subject.
Download or read book Categorical Homological and Combinatorial Methods in Algebra written by Ashish K. Srivastava and published by American Mathematical Soc.. This book was released on 2020-06-23 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the AMS Special Session, in honor of S. K. Jain's 80th birthday, on Categorical, Homological and Combinatorial Methods in Algebra held from March 16–18, 2018, at Ohio State University, Columbus, Ohio. The articles contained in this volume aim to showcase the current state of art in categorical, homological and combinatorial aspects of algebra.
Download or read book Ring Theory and Its Applications written by Dinh Van Huynh and published by American Mathematical Soc.. This book was released on 2014-02-21 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.
Download or read book Serial Rings written by G. Puninski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme in classical ring theory is the structure theory of rings of a particular kind. For example, no one text book in ring theory could miss the Wedderburn-Artin theorem, which says that a ring R is semisimple Artinian iffR is isomorphic to a finite direct sum of full matrix rings over skew fields. This is an example of a finiteness condition which, at least historically, has dominated in ring theory. Ifwe would like to consider a requirement of a lattice-theoretical type, other than being Artinian or Noetherian, the most natural is uni-seriality. Here a module M is called uni-serial if its lattice of submodules is a chain, and a ring R is uni-serial if both RR and RR are uni-serial modules. The class of uni-serial rings includes commutative valuation rings and closed under homomorphic images. But it is not closed under direct sums nor with respect to Morita equivalence: a matrix ring over a uni-serial ring is not uni-serial. There is a class of rings which is very close to uni-serial but closed under the constructions just mentioned: serial rings. A ring R is called serial if RR and RR is a direct sum (necessarily finite) of uni-serial modules. Amongst others this class includes triangular matrix rings over a skew field. Also if F is a finite field of characteristic p and G is a finite group with a cyclic normal p-Sylow subgroup, then the group ring FG is serial.
Download or read book Modules over Commutative Regular Rings written by Richard S. Pierce and published by American Mathematical Soc.. This book was released on 1967 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups Rings And Modules With Applications written by M.R. Adhikari and published by Universities Press. This book was released on 2003 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rings Modules and Linear Algebra written by B. Hartley and published by Chapman and Hall/CRC. This book was released on 1970-09 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of how a certain fundamental algebraic concept can be introduced, developed, and applied to solve some concrete algebraic problems.
