Module Theory Extending Modules And Generalizations

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Module Theory Extending Modules And Generalizations

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Author : Adnan Tercan
language : en
Publisher: Birkhäuser
Release Date : 2016-05-13

Module Theory Extending Modules And Generalizations written by Adnan Tercan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Mathematics categories.

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

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Author : John Clark
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-17

Lifting Modules written by John Clark and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-17 with Mathematics categories.

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules. The text begins with an introduction to small submodules, the radical, variations on projectivity, and hollow dimension. The subsequent chapters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange property and local semi-T-nilpotency), supplements in modules (with specific emphasis on semilocal endomorphism rings), finishing with a long chapter on lifting modules, leading up their use in the theory of perfect rings, Harada rings, and quasi-Frobenius rings. Most of the material in the monograph appears in book form for the first time. The main text is augmented by a plentiful supply of exercises together with comments on further related material and on how the theory has evolved.

Mathematical Methods For Engineering Applications

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Author : Fatih Yilmaz
language : en
Publisher: Springer Nature
Release Date : 2022-04-15

Mathematical Methods For Engineering Applications written by Fatih Yilmaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-15 with Mathematics categories.

This proceedings volume gathers selected, peer-reviewed papers presented at the 2nd International Conference on Mathematics and its Applications in Science and Engineering – ICMASE 2021, which was virtually held on July 1-2, 2021 by the University of Salamanca, Spain. Works included in this book cover applications of mathematics both in engineering research and in real-world problems, touching topics such as difference equations, number theory, optimization, and more. The list of applications includes the modeling of mechanical structures, the shape of machines, and the growth of a population, expanding to fields like information security and cryptography. Advances in teaching and learning mathematics in the context of engineering courses are also covered.This volume can be of special interest to researchers in applied mathematics and engineering fields, as well as practitioners seeking studies that address real-life problems in engineering.

Extensions Of Rings And Modules

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Author : Gary F. Birkenmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-19

Extensions Of Rings And Modules written by Gary F. Birkenmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.

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.

Algebra And Its Applications

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Author : Mohammad Ashraf
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06

Algebra And Its Applications written by Mohammad Ashraf and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Mathematics categories.

This volume showcases mostly the contributions presented at the International Conference in Algebra and Its Applications held at the Aligarh Muslim University, Aligarh, India during November 12-14, 2016. Refereed by renowned experts in the field, this wide-ranging collection of works presents the state of the art in the field of algebra and its applications covering topics such as derivations in rings, category theory, Baer module theory, coding theory, graph theory, semi-group theory, HNP rings, Leavitt path algebras, generalized matrix algebras, Nakayama conjecture, near ring theory and lattice theory. All of the contributing authors are leading international academicians and researchers in their respective fields. Contents On Structure of ∗-Prime Rings with Generalized Derivation A characterization of additive mappings in rings with involution| Skew constacyclic codes over Fq + vFq + v2Fq Generalized total graphs of commutative rings: A survey Differential conditions for which near-rings are commutative rings Generalized Skew Derivations satisfying the second Posner’s theorem on Lie ideals Generalized Skew-Derivations on Lie Ideals in Prime Rings On generalized derivations and commutativity of prime rings with involution On (n, d)-Krull property in amalgamated algebra Pure ideals in ordered Γ-semigroups Projective ideals of differential polynomial rings over HNP rings Additive central m-power skew-commuting maps on semiprime rings A Note on CESS-Lattices Properties Inherited by Direct Sums of Copies of a Module Modules witnessing that a Leavitt path algebra is directly infinite Inductive Groupoids and Normal Categories of Regular Semigroups Actions of generalized derivations in Rings and Banach Algebras Proper Categories and Their Duals On Nakayama Conjecture and related conjectures-Review On construction of global actions for partial actions On 2-absorbing and Weakly 2-absorbing Ideals in Product Lattices Separability in algebra and category theory Annihilators of power values of generalized skew derivations on Lie ideals Generalized derivations on prime rings with involution

Kyungpook Mathematical Journal

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Author :
language : en
Publisher:
Release Date : 2008

Kyungpook Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Analele Universit Ii Din Craiova

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Author :
language : en
Publisher:
Release Date : 2006

Analele Universit Ii Din Craiova written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Information science categories.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards

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Author :
language : en
Publisher:
Release Date : 2005

Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Dissertations, Academic categories.

Algebra Colloquium

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Author :
language : en
Publisher:
Release Date : 2007

Algebra Colloquium written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algebra categories.