Overview
- Brings together both commutative and non-commutative perspectives on multiplicative theory and factorization theory for the first time in one volume?
- Focuses on two significant strands of research in commutative algebra, which represent a long tradition in commutative ring theory
- Contains survey papers by leading experts in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 170)
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About this book
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.
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Keywords
- commutative ring theory
- factorization theory
- multiplicative ideal theory
- non-commutative algebra
- class semigroup
- quasi finite semigroup
- catenary degree
- tame degree
- local tameness
- weakly C-monoid
- coherent domain
- Krull domain
- atomic domain
- HFD
- pseudovaluation domain
- Zariski-Riemann space
- valuation ring
- spectral space
- Dedekind domains
Table of contents (15 papers)
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Front Matter
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Back Matter
Editors and Affiliations
Bibliographic Information
Book Title: Multiplicative Ideal Theory and Factorization Theory
Book Subtitle: Commutative and Non-commutative Perspectives
Editors: Scott Chapman, Marco Fontana, Alfred Geroldinger, Bruce Olberding
Series Title: Springer Proceedings in Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-319-38855-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-38853-3Published: 30 July 2016
Softcover ISBN: 978-3-319-81764-4Published: 30 May 2018
eBook ISBN: 978-3-319-38855-7Published: 29 July 2016
Series ISSN: 2194-1009
Series E-ISSN: 2194-1017
Edition Number: 1
Number of Pages: XIV, 407
Number of Illustrations: 4 b/w illustrations
Topics: Commutative Rings and Algebras, Number Theory, Group Theory and Generalizations, Associative Rings and Algebras, Algebraic Geometry