Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
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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)
  • Received : 2011.10.18
  • Accepted : 2011.12.22
  • Published : 2011.12.30
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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 $\hat{A}$ 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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References

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