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Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes
Book Synopsis Classes of Modules by : John Dauns
Download or read book Classes of Modules written by John Dauns and published by CRC Press. This book was released on 2006-06-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes
This fast-moving tutorial introduces you to OCaml, an industrial-strength programming language designed for expressiveness, safety, and speed. Through the book’s many examples, you’ll quickly learn how OCaml stands out as a tool for writing fast, succinct, and readable systems code. Real World OCaml takes you through the concepts of the language at a brisk pace, and then helps you explore the tools and techniques that make OCaml an effective and practical tool. In the book’s third section, you’ll delve deep into the details of the compiler toolchain and OCaml’s simple and efficient runtime system. Learn the foundations of the language, such as higher-order functions, algebraic data types, and modules Explore advanced features such as functors, first-class modules, and objects Leverage Core, a comprehensive general-purpose standard library for OCaml Design effective and reusable libraries, making the most of OCaml’s approach to abstraction and modularity Tackle practical programming problems from command-line parsing to asynchronous network programming Examine profiling and interactive debugging techniques with tools such as GNU gdb
Book Synopsis Real World OCaml by : Yaron Minsky
Download or read book Real World OCaml written by Yaron Minsky and published by "O'Reilly Media, Inc.". This book was released on 2013-11-04 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fast-moving tutorial introduces you to OCaml, an industrial-strength programming language designed for expressiveness, safety, and speed. Through the book’s many examples, you’ll quickly learn how OCaml stands out as a tool for writing fast, succinct, and readable systems code. Real World OCaml takes you through the concepts of the language at a brisk pace, and then helps you explore the tools and techniques that make OCaml an effective and practical tool. In the book’s third section, you’ll delve deep into the details of the compiler toolchain and OCaml’s simple and efficient runtime system. Learn the foundations of the language, such as higher-order functions, algebraic data types, and modules Explore advanced features such as functors, first-class modules, and objects Leverage Core, a comprehensive general-purpose standard library for OCaml Design effective and reusable libraries, making the most of OCaml’s approach to abstraction and modularity Tackle practical programming problems from command-line parsing to asynchronous network programming Examine profiling and interactive debugging techniques with tools such as GNU gdb
This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
Book Synopsis Module Theory by : Alberto Facchini
Download or read book Module Theory written by Alberto Facchini and published by Springer Science & Business Media. This book was released on 2012-02-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.
This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Book Synopsis Groups, Modules, and Model Theory - Surveys and Recent Developments by : Manfred Droste
Download or read book Groups, Modules, and Model Theory - Surveys and Recent Developments written by Manfred Droste and published by Springer. This book was released on 2017-06-02 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Contains the proceedings of an international conference on abelian groups and modules held recently in Colorado Springs. Presents the latest developments in abelian groups that have facilitated cross-fertilization of new techniques from diverse areas such as the representation theory of posets, model theory, set theory, and module theory.
Book Synopsis Abelian Groups and Modules by : K.M. Rangaswamy
Download or read book Abelian Groups and Modules written by K.M. Rangaswamy and published by CRC Press. This book was released on 1996-08-16 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of an international conference on abelian groups and modules held recently in Colorado Springs. Presents the latest developments in abelian groups that have facilitated cross-fertilization of new techniques from diverse areas such as the representation theory of posets, model theory, set theory, and module theory.
Book Synopsis Scalable and Modular Architecture for CSS by : Jonathan Snook
Download or read book Scalable and Modular Architecture for CSS written by Jonathan Snook and published by . This book was released on 2011-11-27 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Why spend time on coding problems that others have already solved when you could be making real progress on your Ruby project? This updated cookbook provides more than 350 recipes for solving common problems, on topics ranging from basic data structures, classes, and objects, to web development, distributed programming, and multithreading. Revised for Ruby 2.1, each recipe includes a discussion on why and how the solution works. You’ll find recipes suitable for all skill levels, from Ruby newbies to experts who need an occasional reference. With Ruby Cookbook, you’ll not only save time, but keep your brain percolating with new ideas as well. Recipes cover: Data structures including strings, numbers, date and time, arrays, hashes, files and directories Using Ruby’s code blocks, also known as closures OOP features such as classes, methods, objects, and modules XML and HTML, databases and persistence, and graphics and other formats Web development with Rails and Sinatra Internet services, web services, and distributed programming Software testing, debugging, packaging, and distributing Multitasking, multithreading, and extending Ruby with other languages
Book Synopsis Ruby Cookbook by : Lucas Carlson
Download or read book Ruby Cookbook written by Lucas Carlson and published by "O'Reilly Media, Inc.". This book was released on 2015-03-24 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why spend time on coding problems that others have already solved when you could be making real progress on your Ruby project? This updated cookbook provides more than 350 recipes for solving common problems, on topics ranging from basic data structures, classes, and objects, to web development, distributed programming, and multithreading. Revised for Ruby 2.1, each recipe includes a discussion on why and how the solution works. You’ll find recipes suitable for all skill levels, from Ruby newbies to experts who need an occasional reference. With Ruby Cookbook, you’ll not only save time, but keep your brain percolating with new ideas as well. Recipes cover: Data structures including strings, numbers, date and time, arrays, hashes, files and directories Using Ruby’s code blocks, also known as closures OOP features such as classes, methods, objects, and modules XML and HTML, databases and persistence, and graphics and other formats Web development with Rails and Sinatra Internet services, web services, and distributed programming Software testing, debugging, packaging, and distributing Multitasking, multithreading, and extending Ruby with other languages
This book is intended to provide a self-contained account of much of the theory of rings and modules. The theme of the text throughout is the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules. Following a brief outline of the foundations, the book begins with the basic definitions and properties of rings, modules and homomorphisms. The remainder of the text gives comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, decomposition theory, and semiperfect and perfect rings. This second edition includes a chapter containing many of the classical results on Artinian rings that have helped form the foundation for much of contemporary research on the representation theory of Artinian rings and finite-dimensional algebras.
Book Synopsis Rings and Categories of Modules by : Frank W. Anderson
Download or read book Rings and Categories of Modules written by Frank W. Anderson and published by Springer Science & Business Media. This book was released on 1992 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide a self-contained account of much of the theory of rings and modules. The theme of the text throughout is the relationship between the one-sided ideal structure a ring may possess and the behavior of its categories of modules. Following a brief outline of the foundations, the book begins with the basic definitions and properties of rings, modules and homomorphisms. The remainder of the text gives comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, decomposition theory, and semiperfect and perfect rings. This second edition includes a chapter containing many of the classical results on Artinian rings that have helped form the foundation for much of contemporary research on the representation theory of Artinian rings and finite-dimensional algebras.
This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.
Book Synopsis Approximations and Endomorphism Algebras of Modules by : Rüdiger Göbel
Download or read book Approximations and Endomorphism Algebras of Modules written by Rüdiger Göbel and published by Walter de Gruyter. This book was released on 2012-10-01 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.
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.
