The fundamental module of a normal local domain of dimension 2

Yuji Yoshino; Takuji Kawamoto

doi:10.1090/S0002-9947-1988-0957079-7

The fundamental module of a normal local domain of dimension 2

Yuji Yoshino, Takuji Kawamoto

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	425-431
Number of pages	7
Journal	Transactions of the American Mathematical Society
Volume	309
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1988-0957079-7
Publication status	Published - Sep 1988
Externally published	Yes

Keywords

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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10.1090/S0002-9947-1988-0957079-7

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AU - Kawamoto, Takuji

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N2 - 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.

AB - 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.

KW - Auslander-Reiten quivers

KW - Canonical modules

KW - Cohen-Macaulay modules

KW - Local rings

KW - Quotient singularities

KW - Reflexive modules

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

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The fundamental module of a normal local domain of dimension 2

Abstract

Keywords

ASJC Scopus subject areas

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