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Multiplicative Ideal Theory in Commutative Algebra

A Tribute to the Work of Robert Gilmer

  • Conference proceedings
  • © 2006

Overview

Editors:
  1. James W. Brewer

    1. Florida Atlantic University, Boca Raton

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  2. Sarah Glaz

    1. University of Cennecticut, Storrs

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  3. William J. Heinzer

    1. Purdue University, West Lafayette

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  4. Bruce M. Olberding

    1. New Mexico State University, Las Cruces

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  • The entire collection will provide an in-depth overview of the topics of research in a significant and large area of commutative algebra, for the last forty years

  • Includes supplementary material: sn.pub/extras

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Table of contents (26 papers)

  1. Front Matter

    Pages I-XV
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  2. Commutative rngs

    • D. D. Anderson
    Pages 1-20

  3. Robert Gilmer’s work on semigroup rings

    • David F. Anderson
    Pages 21-37

  4. Numerical semigroup algebras

    • Valentina Barucci
    Pages 39-53

  5. Prüfer rings

    • Silvana Bazzoni, Sarah Glaz
    Pages 55-72

  6. Subrings of zero-dimensional rings

    • Jim Brewer, Fred Richman
    Pages 73-88

  7. Old problems and new questions around integer-valued polynomials and factorial sequences

    • Jean-Luc Chabert, Paul-Jean Cahen
    Pages 89-108

  8. Robert Gilmer’s contributions to the theory of integer-valued polynomials

    • Scott T. Chapman, Vadim Ponomarenko, William W. Smith
    Pages 109-122

  9. Progress on the dimension question for power series rings

    • Jim Coykendall
    Pages 123-135

  10. Some research on chains of prime ideals influenced by the writings of Robert Gilmer

    • D. E. Dobbs
    Pages 137-152

  11. Direct-sum decompositions over one-dimensional Cohen-Macaulay local rings

    • Alberto Facchini, Wolfgang Hassler, Lee Klingler, Roger Wiegand
    Pages 153-168

  12. An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations

    • Marco Fontana, K. Alan Loper
    Pages 169-187

  13. Generalized Dedekind domains

    • Stefania Gabelli
    Pages 189-206

  14. Non-unique factorizations: a survey

    • Alfred Geroldinger, Franz Halter-Koch
    Pages 207-226

  15. Mixed polynomial/power series rings and relatinos among their spectra

    • William Heinzer, Christel Rotthaus, Sylvia Wiegand
    Pages 227-242

  16. Uppers to zero in polynomial rings

    • Evan Houston
    Pages 243-261

  17. On the dimension theory of polynomial rings over pullbacks

    • S. Kabbaj
    Pages 263-277

  18. Almost Dedekind domains which are not Dedekind

    • K. Allan Loper
    Pages 279-292

  19. Integrality properties of polynomial rings and semigroup rings

    • Thomas G. Lucas
    Pages 293-309

  20. Punctually free ideals

    • Jack Ohm
    Pages 311-330
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Keywords

About this book

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.

Editors and Affiliations

  • Florida Atlantic University, Boca Raton

    James W. Brewer

  • University of Cennecticut, Storrs

    Sarah Glaz

  • Purdue University, West Lafayette

    William J. Heinzer

  • New Mexico State University, Las Cruces

    Bruce M. Olberding

Bibliographic Information

  • Book Title: Multiplicative Ideal Theory in Commutative Algebra

  • Book Subtitle: A Tribute to the Work of Robert Gilmer

  • Editors: James W. Brewer, Sarah Glaz, William J. Heinzer, Bruce M. Olberding

  • DOI: https://doi.org/10.1007/978-0-387-36717-0

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag US 2006

  • Hardcover ISBN: 978-0-387-24600-0Published: 21 September 2006

  • Softcover ISBN: 978-1-4419-3755-1Published: 29 October 2010

  • eBook ISBN: 978-0-387-36717-0Published: 15 December 2006

  • Edition Number: 1

  • Number of Pages: XV, 435

  • Topics: Algebra, Commutative Rings and Algebras, Group Theory and Generalizations

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