The fundamental module of a normal local domain of dimension 2

Yuji Yoshino, Takuji Kawamoto

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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
Issue number1
Publication statusPublished - Sep 1988
Externally publishedYes


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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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