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Lectures on Rings and Modules
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Joachim Lambek
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Module Theory: An Approach to Linear Algebra
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Tom S Blyth
The aim of this textbook is to develop the basic properties of modules and to show their importance in the theory of linear algebra. It is intended to provide a self-contained course as well as to indicate how the theory may be developed in a number of more advanced directions. Throughout, numerous exercises will enable readers to consolidate ...
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Exercises in Modules and Rings
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T Y Lam
This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
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Lessons on Rings, Modules and Multiplicities
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D G Northcott
This volume provides a clear and self-contained introduction to important results in the theory of rings and modules. Assuming only the mathematical background provided by a normal undergraduate curriculum, the theory is derived by comparatively direct and simple methods. It will be useful to both undergraduates and research students specialising ...
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Introduction to the Theory of Topological Rings and Modules
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V I Arnautov, Arnautov Arnautov, V, S Glavatsky
Provides a thorough introduction to the theory of topological rings and modules--focusing on problems of topologization and extensions of ring topologies.
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Modules and the Structure of Rings: A Primer
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Jonathan S Golan
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Abelian Groups and Modules
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David M Arnold, Rangaswamy Rangaswamy, K M Rangaswamy (Editor)
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.
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Ideals and Reality: Projective Modules and Number of Generators of Ideals
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Friedrich Ischebeck, Ravi A Rao
This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture. The central topic of the book is the question of whether a curve in $n$-space is as a set an intersection of $(n-1 ...
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Modules and Rings
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John Dauns
This book on modern and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The ...
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Algebra: An Approach Via Module Theory
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William A Adkins
This book is designed as a text for a first-year graduate algebra course. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in groups and ring theory, the authors then develop basic module theory, culminating in the fundamental structure theorem for finitely ...
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Torsion-Free Modules
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Eben Matlis
The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an ...
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Almost Free Modules: Set-Theoretic Methods
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A H Meckler, A H Mekler+, Paul C Eklof
This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and up-dated to include ...
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Local Algebra - Multiplicities
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Professor Jean-Pierre Serre, C W Chin (Translator)
This is an English translation of the now classic "Algebre Locale - Multiplicites" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the ...
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Finite Free Resolutions
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D G Northcott, Bela Bollobas (Editor), W Fulton (Editor)
An important part of homological algebra deals with modules possessing projective resolutions of finite length. This goes back to Hilbert's famous theorem on syzygies through, in the earlier theory, free modules with finite bases were used rather than projective modules. The introduction of a wider class of resolutions led to a theory rich in ...
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Auslander-Buchweitz Approximations of Equivariant Modules
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Mitsuyasu Hashimoto, J W S Cassels (Editor), N J Hitchin (Editor)
This book focuses on homological aspects of equivariant modules. It presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of delta-good approximations for quasi-hereditary algebras and reductive groups. The book provides a ...
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Rings, Modules, Algebras, and Abelian Groups
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Facchini Facchini, Alberto Facchini (Editor), Evan Houston (Editor)
"Rings, Modules, Algebras, and Abelian Groups" summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and ...
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Unstable modules over the Steenrod algebra and Sullivan's fixed point set conjecture
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Schwartz
An account of one of the main directions of algebraic topology, this book focuses on the Sullivan conjecture and its generalizations and applications. It gathers work on the theory of modules over the Steenrod algebra, including ideas on the Segal conjecture, work from the late 1970s by Adams and Wilkerson, and topics in algebraic group ...
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Injective Modules and Injective Quotient Rings
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Carl Clifton Faith
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Abelian Groups, Module Theory, and Topology
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A Orsatti, Dikran N Dikranjan, Luigi Salce (Editor)
Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
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Lectures on injective modules and quotient rings
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Carl Faith
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Scientific Ballooning: Technology and Applications of Exploration Balloons Floating in the Stratosphere and the Atmospheres of Other Planets
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Nobuyuki Yajima, Naoki Izutsu, Takeshi Imamura
The aim of this book is to introduce scientific ballooning to the many people who are interested in the use of balloons for scientific applications. The book offers a basic understanding of the engineering details and the scientific research giving rise to balloon activities going on today. Above all, the book will serve as a guidebook for young ...
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FPF ring theory faithful modules and generators of mod-R
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Faith, Page
This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, ...
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An Introduction to Rings and Modules: With K-Theory in View
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A J Berrick, M E Keating, Bela Bollobas (Editor)
This is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It ...
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Model Theory and Modules
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by
Prest
In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model ...
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Introduction to Vertex Operator Superalgebras and Their Modules
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Xiaoping Xu
This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator ...
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