Extending Modules

Extending Modules

Author: Nguyen Viet Dung

Publisher: Routledge

Published: 2019-01-22

Total Pages: 286

ISBN-13: 1351449087

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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


Book Synopsis Extending Modules by : Nguyen Viet Dung

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

Extending Modules

Extending Modules

Author: Nguyen Viet Dung

Publisher: Routledge

Published: 2019-01-22

Total Pages: 248

ISBN-13: 1351449095

DOWNLOAD EBOOK

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


Book Synopsis Extending Modules by : Nguyen Viet Dung

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 248 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

Module Theory, Extending Modules and Generalizations

Module Theory, Extending Modules and Generalizations

Author: Adnan Tercan

Publisher: Birkhäuser

Published: 2016-05-13

Total Pages: 369

ISBN-13: 3034809522

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The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.


Book Synopsis Module Theory, Extending Modules and Generalizations by : Adnan Tercan

Download or read book Module Theory, Extending Modules and Generalizations written by Adnan Tercan and published by Birkhäuser. This book was released on 2016-05-13 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area. Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises.

Lifting Modules

Lifting Modules

Author: John Clark

Publisher: Springer Science & Business Media

Published: 2008-08-17

Total Pages: 403

ISBN-13: 3764375736

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Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.


Book Synopsis Lifting Modules by : John Clark

Download or read book Lifting Modules written by John Clark and published by Springer Science & Business Media. This book was released on 2008-08-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.

Extensions of Rings and Modules

Extensions of Rings and Modules

Author: Gary F. Birkenmeier

Publisher: Springer Science & Business Media

Published: 2013-07-19

Total Pages: 442

ISBN-13: 0387927166

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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.


Book Synopsis Extensions of Rings and Modules by : Gary F. Birkenmeier

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.

Rings, Modules and Codes

Rings, Modules and Codes

Author: André Leroy

Publisher: American Mathematical Soc.

Published: 2019-04-12

Total Pages: 355

ISBN-13: 1470441047

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This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.


Book Synopsis Rings, Modules and Codes by : André Leroy

Download or read book Rings, Modules and Codes written by André Leroy and published by American Mathematical Soc.. This book was released on 2019-04-12 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.

Abelian Groups and Modules

Abelian Groups and Modules

Author: Paul C. Eklof

Publisher: Birkhäuser

Published: 2013-04-17

Total Pages: 374

ISBN-13: 3034875916

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A 30-article volume, introducing an active and attractive part of algebra that has gained much from its position at the crossroads of mathematics over the years. The papers stimulate the reader to consider and actively investigate the topics and problems they contain.


Book Synopsis Abelian Groups and Modules by : Paul C. Eklof

Download or read book Abelian Groups and Modules written by Paul C. Eklof and published by Birkhäuser. This book was released on 2013-04-17 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 30-article volume, introducing an active and attractive part of algebra that has gained much from its position at the crossroads of mathematics over the years. The papers stimulate the reader to consider and actively investigate the topics and problems they contain.

Advances in Rings and Modules

Advances in Rings and Modules

Author: Sergio R. López-Permouth

Publisher: American Mathematical Soc.

Published: 2018-09-06

Total Pages: 283

ISBN-13: 1470435551

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This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.


Book Synopsis Advances in Rings and Modules by : Sergio R. López-Permouth

Download or read book Advances in Rings and Modules written by Sergio R. López-Permouth and published by American Mathematical Soc.. This book was released on 2018-09-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.

Advances in Ring Theory

Advances in Ring Theory

Author: S.K. Jain

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 330

ISBN-13: 1461219787

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Book Synopsis Advances in Ring Theory by : S.K. Jain

Download or read book Advances in Ring Theory written by S.K. Jain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Journal of Zhejiang University

Journal of Zhejiang University

Author:

Publisher:

Published: 2007

Total Pages: 504

ISBN-13:

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Book Synopsis Journal of Zhejiang University by :

Download or read book Journal of Zhejiang University written by and published by . This book was released on 2007 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: