WorldCat Identities

Geroldinger, Alfred

Overview
Works: 8 works in 42 publications in 1 language and 984 library holdings
Roles: Author, Editor
Classifications: QA247, 512.74
Publication Timeline
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Most widely held works by Alfred Geroldinger
Non-unique factorizations : algebraic, combinatorial and analytic theory by Alfred Geroldinger( Book )

15 editions published in 2006 in English and Undetermined and held by 186 WorldCat member libraries worldwide

Geroldinger and Halter-Koch, both professors of mathematics at Karl Franzens University in Austria, outline the present state of the theory of non-unique factorizations and discuss related algebraic, combinatorial, and analytic fundamentals. The introductory chapter is accessible to readers with background in standard basic algebra. Coverage then m
Combinatorial number theory and additive group theory by Alfred Geroldinger( Book )

17 editions published in 2009 in English and Undetermined and held by 126 WorldCat member libraries worldwide

This book collects the material delivered in the 2008 edition of the DocCourse in Combinatorics and Geometry which was devoted to the topic of additive combinatorics. The first two parts, which form the bulk of the volume, contain the two main advanced courses, Additive Group Theory and Non-Unique Factorizations by Alfred Geroldinger, and Sumsets and Structure by Imre Z. Ruzsa. The first part centers on the interaction between non-unique factorization theory and additive group theory. The main objective of factorization theory is a systematic treatment of phenomena related to the non-uniqueness of factorizations in monoids and domains. This part introduces basic concepts of factorization theory such as sets of lengths, and outlines the translation of arithmetical questions in Krull monoids into combinatorial questions on zero-sum sequences over the class group. Using methods from additive group theory such as the theorems of Kneser and of Kemperman-Scherk, classical zero-sum constants are studied, including the Davenport constant and the Erdös-Ginzburg-Ziv constant. Finally these results are applied again to the starting arithmetical problems. The second part is a course on the basics of combinatorial number theory (or additive combinatorics): cardinality inequalities (Plünnecke{u2019}s graph theoretical method), Freiman{u2019}s theorem on the structure of sets with a small sumset, inequalities for the Schnirelmann and asymptotic density of sumsets, analogous results for the measure of sumsets of reals, the connection with the Bohr topology. The third part of the volume collects some of the seminars which accompanied the main courses. It contains contributions by C. Elsholtz, G. Freiman, Y.O. Hamidoune, N. Hegyvari, G. Karolyi, M. Nathanson, J. Solymosi and Y. Stanchescu
Multiplicative Ideal Theory and Factorization Theory Commutative and Non-commutative Perspectives by Scott T Chapman( Book )

5 editions published in 2016 in English and held by 3 WorldCat member libraries worldwide

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- 6, 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
Chains of factorizations in orders of global fields by Alfred Geroldinger( )

1 edition published in 1997 in English and held by 1 WorldCat member library worldwide

Congruence monoids by Alfred Geroldinger( )

1 edition published in 2004 in English and held by 1 WorldCat member library worldwide

Inverse zero-sum problems by Weidong Gao( )

1 edition published in 2007 in English and held by 1 WorldCat member library worldwide

A structure theorem for sets of lengths by Alfred Geroldinger( )

1 edition published in 1998 in English and held by 1 WorldCat member library worldwide

Chains of factorizations in weakly Krull domains by Alfred Geroldinger( )

1 edition published in 1997 in English and held by 1 WorldCat member library worldwide

 
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Audience level: 0.61 (from 0.52 for Combinator ... to 0.99 for Inverse ze ...)

Non-unique factorizations : algebraic, combinatorial and analytic theory
Languages
English (40)

Covers
Combinatorial number theory and additive group theory