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
.
Most widely held works by
Alfred Geroldinger
Nonunique 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 HalterKoch, both professors of mathematics at Karl Franzens University in Austria, outline the present state of the theory of nonunique 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
15 editions published in 2006 in English and Undetermined and held by 186 WorldCat member libraries worldwide
Geroldinger and HalterKoch, both professors of mathematics at Karl Franzens University in Austria, outline the present state of the theory of nonunique 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 NonUnique Factorizations by Alfred Geroldinger, and Sumsets and Structure by Imre Z. Ruzsa. The first part centers on the interaction between nonunique factorization theory and additive group theory. The main objective of factorization theory is a systematic treatment of phenomena related to the nonuniqueness 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 zerosum sequences over the class group. Using methods from additive group theory such as the theorems of Kneser and of KempermanScherk, classical zerosum constants are studied, including the Davenport constant and the ErdösGinzburgZiv 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
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 NonUnique Factorizations by Alfred Geroldinger, and Sumsets and Structure by Imre Z. Ruzsa. The first part centers on the interaction between nonunique factorization theory and additive group theory. The main objective of factorization theory is a systematic treatment of phenomena related to the nonuniqueness 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 zerosum sequences over the class group. Using methods from additive group theory such as the theorems of Kneser and of KempermanScherk, classical zerosum constants are studied, including the Davenport constant and the ErdösGinzburgZiv 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 Noncommutative 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 noncommutative 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 integervalued 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
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 noncommutative 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 integervalued 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
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
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Inverse zerosum problems by
Weidong Gao(
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
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
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
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
Audience Level
0 

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Kids  General  Special 
Related Identities
 Ruzsa, Imre
 HalterKoch, Franz 1944 Other
 Fontana, Marco 1947 Editor
 Olberding, Bruce Editor
 Chapman, Scott T. Editor
 Ruzsa, Imre Z. Author
 Castellet, Manuel Author
 Centre de Recerca Matemàtica <Barcelona>
 Schmid, Wolfgang A.
 Gao, Weidong (1967 ). Author
Associated Subjects