Multiplicative Ideal Theory in Commutative Algebra: A Tribute to the Work of Robert Gilmer / Edition 1

Paperback (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $110.24
Usually ships in 1-2 business days
(Save 26%)
Other sellers (Paperback)
  • All (7) from $110.24   
  • New (6) from $110.24   
  • Used (1) from $187.98   

More About This Textbook


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.

Read More Show Less

Product Details

  • ISBN-13: 9781441937551
  • Publisher: Springer US
  • Publication date: 10/29/2010
  • Edition description: Softcover reprint of hardcover 1st ed. 2006
  • Edition number: 1
  • Pages: 435
  • Product dimensions: 0.91 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

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

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)