통합자연과학논문집 (Journal of Integrative Natural Science)

조선대학교 기초과학연구원 (The Basic Science Institute Chosun University)
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Restrictions on the Entries of the Maps in Free Resolutions and $SC_r$-condition

  • Lee, Kisuk (Department of Mathematics, Sookmyung Women's University)
  • 투고 : 2011.10.18
  • 심사 : 2011.12.22
  • 발행 : 2011.12.30
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초록

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 $\hat{A}$ has no embedded primes. If A is not Gorenstein, then ${\mu}_i(m,A){\geq}2$ for all i ${\geq}$ dimA.

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참고문헌

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