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http://dx.doi.org/10.13160/ricns.2011.4.4.278

Restrictions on the Entries of the Maps in Free Resolutions and $SC_r$-condition  

Lee, Kisuk (Department of Mathematics, Sookmyung Women's University)
Publication Information
Journal of Integrative Natural Science / v.4, no.4, 2011 , pp. 278-281 More about this Journal
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.
Keywords
Bass Numbers; $SC_r$-condition; Cohen-Macaulay Rings; Gorenstein Rings; Minimal Injective Resolution;
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