Multiplicative Ideal Theory in Commutative Algebra: A Tribute to the Work of Robert Gilmer

ISBN-13: 9781441937551 / Angielski / Miękka / 2010 / 435 str.

James W. Brewer; Sarah Glaz; William Heinzer

Opis

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."

Spis treści

Preface Commutative rngs (D. D. Anderson) Robert Gilmer’s work on semigroup rings (David F. Anderson) Numerical semigroup algebras (Valentina Barucci) Prüfer rings (Silvana Bazzoni, Sarah Glaz) Subrings of zero-dimensional rings (Jim Brewer, Fred Richman) Old problems and new questions around integer-valued polynomials and factorial sequences (Jean-Luc Chabert, Paul-Jean Cahen) Robert Gilmer’s contributions to the theory of integer-valued polynomials (Scott T. Chapman, Vadim Ponomarenko, William W. Smith) Progress on the dimension question for power series rings (Jim Coykendall) Some research on chains of prime ideals influenced by the writings of Robert Gilmer (D. E. Dobbs) Direct-sum decompositions over one-dimensional Cohen-Macaulay local rings (Alberto Facchini, Wolfgang Hassler, Lee Klingler, Roger Wiegand) An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations (Marco Fontana, K. Alan Loper) Generalized Dedekind domains (Stefania Gabelli) Non-unique factorizations: a survey (Alfred Geroldinger, Franz Halter-Koch) Mixed polynomial/power series rings and relations among their spectra (William Heinzer, Christel Rotthaus, Sylvia Wiegand) Uppers to zero in polynomial rings (Evan Houston) On the dimension theory of polynomial rings over pullbacks (S. Kabbaj) Almost Dedekind domains which are not Dedekind (K. Alan Loper) Integrality properties of polynomial rings and semigroup rings (Thomas G. Lucas) Punctually free ideals (Jack Ohm) Holomorphy rings of function fields (Bruce Olberding) The minimal number of generators of an invertible ideal (Bruce Olberding, Moshe Roitman) About minimal morphisms (Gabriel Picavet, Martine Picavet-L’Hermitte) What v-coprimality can do for you (Muhammad Zafrullah) Somequestions for further research (Robert Gilmer) Robert Gilmer’s published works Commutative Algebra at Florida State 1963–1968 (Jim Brewer, Bill Heinzer) Index

O autorze

For over 40 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-Noeotherian 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 articles by some of the most prominent experts in the field. These articles combine in various degrees surveys of past work, by Gilmer and others, recent results which had never before seen print, open problems, and an extensive bibliography. In a concluding article, Gilmer points out directions for future research, highlighting the open problems in the areas he considers of importance. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra, covering the last forty years.

Blurb

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.

Audience

This book is intended for researchers and graduate students in the field of commutative algebra.