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 - 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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Cite this
Yoshino, Y., & Kawamoto, T. (1988). The fundamental module of a normal local domain of dimension 2. Transactions of the American Mathematical Society, 309(1), 425-431. https://doi.org/10.1090/S0002-9947-1988-0957079-7