Arithmetical Properties of Commutative Rings and Monoids
Arithmetical Properties of Commutative Rings and Monoids

Author: Scott T. Chapman

Publisher: CRC Press

Published: 2005-03-01

Total Pages: 410

ISBN-13: 1420028243

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The study of nonunique factorizations of elements into irreducible elements in commutative rings and monoids has emerged as an independent area of research only over the last 30 years and has enjoyed a recent flurry of activity and advancement. This book presents the proceedings of two recent meetings that gathered key researchers from around the w

Finitely Generated Commutative Monoids
Finitely Generated Commutative Monoids

Author: J. C. Rosales

Publisher: Nova Publishers

Published: 1999

Total Pages: 204

ISBN-13: 9781560726708

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A textbook for an undergraduate course, requiring only a knowledge of basic linear algebra. Explains how to compute presentations for finitely generated cancellative monoids, and from a presentation of a monoid, decide whether this monoid is cancellative, reduced, separative, finite, torsion free, group, affine, full, normal, etc. Of most interest to people working with semigroup theory, but also in other areas of algebra. Annotation copyrighted by Book News, Inc., Portland, OR

Non-Unique Factorizations
Non-Unique Factorizations

Author: Alfred Geroldinger

Publisher: CRC Press

Published: 2006-01-13

Total Pages: 723

ISBN-13: 1420003208

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From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza

Arithmetical Rings and Endomorphisms
Arithmetical Rings and Endomorphisms

Author: Askar Tuganbaev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-06-04

Total Pages: 176

ISBN-13: 3110659824

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This book offers a comprehensive account of not necessarily commutative arithmetical rings, examining structural and homological properties of modules over arithmetical rings and summarising the interplay between arithmetical rings and other rings, whereas modules with extension properties of submodule endomorphisms are also studied in detail. Graduate students and researchers in ring and module theory will find this book particularly valuable.

Multiplicative Ideal Theory and Factorization Theory
Multiplicative Ideal Theory and Factorization Theory

Author: Scott Chapman

Publisher: Springer

Published: 2016-07-29

Total Pages: 414

ISBN-13: 331938855X

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This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

Advances in Commutative Algebra
Advances in Commutative Algebra

Author: Ayman Badawi

Publisher: Springer

Published: 2019-04-11

Total Pages: 280

ISBN-13: 9811370281

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This book highlights the contributions of the eminent mathematician and leading algebraist David F. Anderson in wide-ranging areas of commutative algebra. It provides a balance of topics for experts and non-experts, with a mix of survey papers to offer a synopsis of developments across a range of areas of commutative algebra and outlining Anderson’s work. The book is divided into two sections—surveys and recent research developments—with each section presenting material from all the major areas in commutative algebra. The book is of interest to graduate students and experienced researchers alike.

Non-Noetherian Commutative Ring Theory
Non-Noetherian Commutative Ring Theory

Author: S.T. Chapman

Publisher: Springer Science & Business Media

Published: 2000-10-31

Total Pages: 504

ISBN-13: 9780792364924

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This volume consists of twenty-one articles by many of the most prominent researchers in non-Noetherian commutative ring theory. The articles combine in various degrees surveys of past results, recent results that have never before seen print, open problems, and an extensive bibliography. One hundred open problems supplied by the authors have been collected in the volume's concluding chapter. The entire collection provides a comprehensive survey of the development of the field over the last ten years and points to future directions of research in the area. Audience: Researchers and graduate students; the volume is an appropriate source of material for several semester-long graduate-level seminars and courses.

Commutative Algebra
Commutative Algebra

Author: Marco Fontana

Publisher: Springer

Published: 2014-07-15

Total Pages: 372

ISBN-13: 1493909258

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This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.

Multiplicative Ideal Theory in Commutative Algebra
Multiplicative Ideal Theory in Commutative Algebra

Author: James W. Brewer

Publisher: Springer Science & Business Media

Published: 2006-12-15

Total Pages: 437

ISBN-13: 0387367179

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This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.

Number Theory and Applications
Number Theory and Applications

Author: S.D. Adhikari

Publisher: Springer

Published: 2009-06-15

Total Pages: 285

ISBN-13: 9386279460

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This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.