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Restrictions on the Entries of the Maps in Free Resolutions and $SC_r$-condition
Lee, Kisuk The Basic Science Institute Chosun University 2011 조선자연과학논문집 Vol.4 No.4
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.
Restrictions on the Entries of the Maps in Free Resolutions and SC_r-condition
이기석 조선대학교 기초과학연구원 2011 조선자연과학논문집 Vol.4 No.4
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.
MAPS IN MINIMAL INJECTIVE RESOLUTIONS OF MODULES
Lee, Ki-Suk Korean Mathematical Society 2009 대한수학회보 Vol.46 No.3
We investigate the behavior of maps in minimal injective resolution of an A-module M when ${\mu}_t$(m,M) = 1 for some t, and we develop slightly the fact that a module of type 1 is Cohen-Macaulay.
Maps in minimal injective resolutions of modules
이기석 대한수학회 2009 대한수학회보 Vol.46 No.3
We investigate the behavior of maps in minimal injective resolution of an A-module M when μ_(t)(m,M)=1 for some t, and we develop slightly the fact that a module of type 1 is Cohen-Macaulay.