Bruce Olberding – författare

For over forty years, Robert Gilmer’s numerous articles and books have had a tremendous impact on research in commutative algebra. It is not an exaggeration to say that most articles published today in non-Noetherian ring theory, and some in Noetherian ring theory as well, originated in a topic that Gilmer either initiated or enriched by his work. This volume, a tribute to his work, consists of twenty-four articles authored by Robert Gilmer’s most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. In a concluding article, Robert Gilmer points out directions for future research, highlighting the open problems in the areas he considers of importance. Robert Gilmer’s article is followed by the complete list of his published works, his mathematical genealogical tree, information on the writing of his four books, and reminiscences about Robert Gilmer’s contributions to the stimulating research environment in commutative algebra at Florida State in the middle 1960s. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.

Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra.

This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others.

This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.

This proceedings volume gathers a selection of cutting-edge research in both commutative and non-commutative ring theory and factorization theory. The papers were presented at the Conference on Rings and Factorization held at the University of Graz, Austria, July 10–14, 2023. The volume covers a wide range of topics including multiplicative ideal theory, Dedekind, Prüfer, Krull, and Mori rings, non-commutative rings and algebras, rings of integer-valued polynomials, topological aspects in ring theory, factorization theory in rings and semigroups, and direct-sum decomposition of modules. The conference also featured two special sessions dedicated to Matej Brešar and Sophie Frisch on the occasion of their 60th birthdays.

This volume is aimed at graduate students and researchers in these areas as well as related fields and provides new insights into both classical and contemporary research in ring and factorization theory.

This volume contains selected refereed papers based on lectures presented at the ‘Fifth International Fez Conference on Commutative Algebra and Applications’ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.

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.