On vanishing of certain Ext modules

Shiro Goto, Futoshi Hayasaka, Ryo Takahashi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Let R be a Noetherian local ring with the maximal ideal m and dimR = 1. In this paper, we shall prove that the module Ext1R does not vanish for every parameter ideal Q in R, if the embedding dimension v(R) of R is at most 4 and the ideal m2 kills the Oth local cohomology module Hom(R). The assertion is no longer true unless v(R) ≤ 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.

Original languageEnglish
Pages (from-to)1045-1064
Number of pages20
JournalJournal of the Mathematical Society of Japan
Issue number4
Publication statusPublished - Oct 2008
Externally publishedYes


  • G-dimension
  • Parameter ideal
  • Vanishing of Ext

ASJC Scopus subject areas

  • Mathematics(all)


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