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 | |
| Publication status | Published - 1988 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - The fundamental module of a normal local domain of dimension 2
AU - Yoshino, Yuji
AU - Kawamoto, Takuji
PY - 1988
Y1 - 1988
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
UR - http://www.scopus.com/inward/record.url?scp=0001548296&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0001548296&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1988-0957079-7
DO - 10.1090/S0002-9947-1988-0957079-7
M3 - Article
AN - SCOPUS:0001548296
VL - 309
SP - 425
EP - 431
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 1
ER -