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Power Series over Commutative Rings

Power Series over Commutative Rings
Author: Brewer
Publisher: CRC Press
Total Pages: 118
Release: 1981-04-01
Genre: Mathematics
ISBN: 9780824769529

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Introduction To Commutative Algebra

Introduction To Commutative Algebra
Author: Michael F. Atiyah
Publisher: CRC Press
Total Pages: 140
Release: 2018-03-09
Genre: Mathematics
ISBN: 0429973268

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First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.


Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples

Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples
Author: William Heinzer
Publisher: American Mathematical Soc.
Total Pages: 426
Release: 2021-10-08
Genre: Education
ISBN: 1470466422

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Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.


Commutative Algebra

Commutative Algebra
Author: Marco Fontana
Publisher: Springer
Total Pages: 372
Release: 2014-07-15
Genre: Mathematics
ISBN: 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.


Linear Algebra over Commutative Rings

Linear Algebra over Commutative Rings
Author: Bernard R. McDonald
Publisher: CRC Press
Total Pages: 563
Release: 2020-11-26
Genre: Mathematics
ISBN: 1000146464

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This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.


Advances in Commutative Ring Theory

Advances in Commutative Ring Theory
Author: David Dobbs
Publisher: CRC Press
Total Pages: 578
Release: 1999-03-04
Genre: Mathematics
ISBN: 9780824771478

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"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."


Topics in the Homological Theory of Modules Over Commutative Rings

Topics in the Homological Theory of Modules Over Commutative Rings
Author: Melvin Hochster
Publisher: American Mathematical Soc.
Total Pages: 86
Release: 1975
Genre: Mathematics
ISBN: 0821816748

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Contains expository lectures from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. This book deals mainly with developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings.


Commutative Ring Theory

Commutative Ring Theory
Author: Paul-Jean Cahen
Publisher: CRC Press
Total Pages: 489
Release: 2023-06-14
Genre: Mathematics
ISBN: 1000946762

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Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.


Commutative Ring Theory

Commutative Ring Theory
Author: Cahen
Publisher: CRC Press
Total Pages: 278
Release: 1993-10-28
Genre: Mathematics
ISBN: 9780824791704

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" Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more!"