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Restrictions on the Entries of the Maps in Free Resolutions and SC_r-condition
- Authors
- 이기석
- Issue Date
- Dec-2011
- Publisher
- 조선대학교 기초과학연구원
- Keywords
- Bass Numbers; SCr-condition; Cohen-Macaulay Rings; Gorenstein Rings; Minimal Injective Resolution
- Citation
- 조선자연과학논문집, v.4, no.4, pp 278 - 281
- Pages
- 4
- Journal Title
- 조선자연과학논문집
- Volume
- 4
- Number
- 4
- Start Page
- 278
- End Page
- 281
- ISSN
- 2005-1042
- Abstract
- We discuss an application of ‘restrictions on the entries of the maps in the minimal free resolution‘ and ‘SC_r-condition of modules’, and give an alternative proof of the following result of Foxby: Let M be a finitely generated module of dimension over a Noetherian local ring (A,m). Suppose that A has no embedded primes. If A is not Gorenstein, then μi(m,A) ≥ 2 for all i ≥ dimA.
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