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Extending Modules

2019-01-22 Mathematics
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Release : 2019-01-22
Genre : Mathematics
Kind : eBook
Book Rating : 087/5 ( reviews)

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Book Synopsis Extending Modules by : Nguyen Viet Dung

Download or read book Extending Modules written by Nguyen Viet Dung. This book was released on 2019-01-22. 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

2019-01-22 Mathematics
Download Extending Modules PDF Online Free

Author :
Release : 2019-01-22
Genre : Mathematics
Kind : eBook
Book Rating : 095/5 ( reviews)

GET EBOOK


Book Synopsis Extending Modules by : Nguyen Viet Dung

Download or read book Extending Modules written by Nguyen Viet Dung. This book was released on 2019-01-22. 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

2016-05-13 Mathematics
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Release : 2016-05-13
Genre : Mathematics
Kind : eBook
Book Rating : 522/5 ( reviews)

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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. This book was released on 2016-05-13. 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

2008-08-17 Mathematics
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Release : 2008-08-17
Genre : Mathematics
Kind : eBook
Book Rating : 736/5 ( reviews)

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Book Synopsis Lifting Modules by : John Clark

Download or read book Lifting Modules written by John Clark. This book was released on 2008-08-17. 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

2013-07-19 Mathematics
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Release : 2013-07-19
Genre : Mathematics
Kind : eBook
Book Rating : 166/5 ( reviews)

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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. This book was released on 2013-07-19. 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.

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