Multiplicative Ideal Theory and Factorization Theory: Commutative and Non-commutative Perspectives

✍ Scribed by Scott Chapman, Marco Fontana, Alfred Geroldinger, Bruce Olberding (eds.)

Publisher: Springer International Publishing
Year: 2016
Tongue: English
Leaves: 414
Series: Springer Proceedings in Mathematics & Statistics 170
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiv
Multiplicative Ideal Theory in Noncommutative Rings....Pages 1-21
About Number Fields with Pólya Group of Order (\le ) 2....Pages 23-42
The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics....Pages 43-95
Ring and Semigroup Constructions....Pages 97-115
New Distinguished Classes of Spectral Spaces: A Survey....Pages 117-143
Relative Polynomial Closure and Monadically Krull Monoids of Integer-Valued Polynomials....Pages 145-157
An Overview of the Computational Aspects of Nonunique Factorization Invariants....Pages 159-181
Arithmetic of Mori Domains and Monoids: The Global Case....Pages 183-218
Prüfer Domains of Integer-Valued Polynomials....Pages 219-231
Lobal Properties of Integral Domains....Pages 233-254
Noetherian Semigroup Algebras and Beyond....Pages 255-276
Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings....Pages 277-307
Idempotent Pairs and PRINC Domains....Pages 309-322
Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group....Pages 323-352
Factorizations of Elements in Noncommutative Rings: A Survey....Pages 353-402
Back Matter....Pages 403-407

✦ Subjects

Commutative Rings and Algebras;Number Theory;Group Theory and Generalizations;Associative Rings and Algebras;Algebraic Geometry

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