Download or read book Theory of Clean Rings and Matrices written by Huanyin Chen and published by World Scientific Publishing Company. This book was released on 2022-09-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to clean ring and matrix theory. It aims to study a theory of expressing an element in a ring as the sum of some special ones, such as idempotents, units, nilpotents, tripotents, involutions, etc. A matrix over such rings is thereby expressed as the sum of some special matrices. Also another topics on the behaviors of topological properties and *-properties of such rings are investigated.The book is based on the results of various published papers, particularly, by the authors'. It is accessible for students familiar with general abstract algebra, while the topics are interesting for researchers in the field of ring, matrix and operator theory.
Download or read book Theory Of Clean Rings And Matrices written by Huanyin Chen and published by World Scientific. This book was released on 2022-08-30 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to clean ring and matrix theory. It aims to study a theory of expressing an element in a ring as the sum of some special ones, such as idempotents, units, nilpotents, tripotents, involutions, etc. A matrix over such rings is thereby expressed as the sum of some special matrices. Also another topics on the behaviors of topological properties and *-properties of such rings are investigated.The book is based on the results of various published papers, particularly, by the authors'. It is accessible for students familiar with general abstract algebra, while the topics are interesting for researchers in the field of ring, matrix and operator theory.
Download or read book Formal Matrices written by Piotr Krylov and published by Springer. This book was released on 2017-03-30 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a solid understanding of basic algebra.
Download or read book Rings Related to Stable Range Conditions written by Huanyin Chen and published by World Scientific. This book was released on 2011 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.
Download or read book Methods in Ring Theory written by Vesselin Drensky and published by CRC Press. This book was released on 2021-02-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."
Download or read book Methods in Ring Theory written by Vesselin Drensky and published by CRC Press. This book was released on 1998-03-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."
Download or read book Advances in Ring Theory written by Sergio R. López-Permouth and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.
Download or read book Radical Theory of Rings written by J.W. Gardner and published by CRC Press. This book was released on 2003-11-19 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Radical Theory of Rings distills the most noteworthy present-day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Assimilating radical theory's evolution in the decades since the last major work on rings and radicals was published, the authors deal with some distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near-rings. Written in clear algebraic terms by globally acknowledged authorities, the presentation includes more than 500 landmark and up-to-date references providing direction for further research.
Download or read book Matrices over Commutative Rings written by William Brown and published by CRC Press. This book was released on 1992-11-23 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to cover the most important aspects of the theory of matrices whose entries come from a given commutative ring. Essential facts about commutative rings are developed throughout the book, and proofs that follow from concrete matrix calculations are also provided.
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 Linear Algebra and Matrix Theory written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-10-17 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.
Download or read book Theory of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and published by CRC Press. This book was released on 2003-09-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular elements in a ring, regular matrices over principal ideal rings, and regular matrices over commutative rings. Students, mathematicians working in g-inverses of matrices, along with algebraists, and control theorists will find new and indispensable data, presented with clarity and insight. This book is also well suited to graduate courses on g-inverses in algebra.
Download or read book Ring Theory written by Kenneth Goodearl and published by CRC Press. This book was released on 1976-03-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Ring Theory written by J L Chen and published by World Scientific. This book was released on 2005-08-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the various areas of ring and module theory — ideal for researchers looking for a new or related field of study. Also included are original articles showing the trend of current research. Contents:Constructing Morphic Rings (J-L Chen et al.)Rings Whose Simple Modules Have Some Properties (Y Hirano)On a Left H-Ring with Nakayama Automorphism (J Kado)On Lifting Properties of Modules (Y Kuratomi)A Survey of Morphic Modules and Rings (W K Nicholson)Flat Cover and Cotorsion Envelope Commute (P Rothmaler)From Galois Field Extensions to Galois Comodules (R Wisbauer)Galois Coverings of Selfinjective Algebras by Twisted Repetitive Algebras (K Yamagata)and other papers Readership: Algebraists in particular non-commutative ring theorists. Keywords:Perspective Survey;Diversified;Distinctive (Articles);Current Field;Distinguished Invited Speakers
Download or read book Noncommutative Rings Group Rings Diagram Algebras and Their Applications written by Surender Kumar Jain and published by American Mathematical Soc.. This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this volume are based on talks given at the International Conference on Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications. The conference provided researchers in mathematics with the opportunity to discuss new developments in these rapidly growing fields. This book contains several excellent articles, both expository and original, with new and significant results. It is suitable for graduate students and researchers interested in Ring Theory,Diagram Algebras and related topics.
Download or read book Algebraic Theory of Generalized Inverses written by Jianlong Chen and published by Springer Nature. This book was released on with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Determinantal Rings written by Winfried Bruns and published by Springer. This book was released on 2006-11-14 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.
