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

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Scott Chapman, Marco Fontana, Alfred Geroldinger, Bruce Olberding
Springer, Jul 29, 2016 - Mathematics - 407 pages

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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Contents

Multiplicative Ideal Theory in Noncommutative Rings
1
About Number Fields with Pólya Group of Order leq2
23
The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics
43
Ring and Semigroup Constructions
96
A Survey
117
Relative Polynomial Closure and Monadically Krull Monoids of IntegerValued Polynomials
144
An Overview of the Computational Aspects of Nonunique Factorization Invariants
159
The Global Case
182
Lobal Properties of Integral Domains
233
Noetherian Semigroup Algebras and Beyond
255
Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings
277
Idempotent Pairs and PRINC Domains
308
Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group
323
A Survey
353
Index
403
Copyright

Prüfer Domains of IntegerValued Polynomials
219

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