The fundamental module of a normal local domain of dimension 2

Yuji Yoshino, Takuji Kawamoto

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The fundamental module E of a normal local domain (R, m) of dimension 2 is defined by the nonsplit exact sequence 0—> K —> E —► m —► 0, where K is the canonical module of R. (Formula presented) We prove that, if R is complete with R/m ˜ C, then E is decomposable if and only if R is a cyclic quotient singularity. Various other properties of fundamental modules will be discussed.

Original languageEnglish
Pages (from-to)425-431
Number of pages7
JournalTransactions of the American Mathematical Society
Volume309
Issue number1
DOIs
Publication statusPublished - 1988
Externally publishedYes

Fingerprint

Canonical Module
Module
Exact Sequence
Decomposable
Quotient
Singularity
If and only if

Keywords

  • Auslander-Reiten quivers
  • Canonical modules
  • Cohen-Macaulay modules
  • Local rings
  • Quotient singularities
  • Reflexive modules

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The fundamental module of a normal local domain of dimension 2. / Yoshino, Yuji; Kawamoto, Takuji.

In: Transactions of the American Mathematical Society, Vol. 309, No. 1, 1988, p. 425-431.

Research output: Contribution to journalArticle

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