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A NOTE ON BETTI NUMBERS AND RESOLUTIONS
Choi, Sang-Ki Korean Mathematical Society 1997 대한수학회논문집 Vol.12 No.4
We study the Betti numbers, the Bass numbers and the resolution of modules under the change of rings. For modules of finite homological dimension, we study the Euler characteristic of them.
DUAL BASS NUMBERS AND CO-COHEN MACAULAY MODULES
Li, Lingguang Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
In this paper, we show that the co-localization of co-Cohen Macaulay modules preserves co-Cohen Macaulayness under a certain condition. In addition, we give a characterization of co-Cohen Macaulay modules by vanishing properties of the dual Bass numbers of modules.
Dual bass numbers and co-Cohen Macaulay modules
Lingguang Li 대한수학회 2018 대한수학회보 Vol.55 No.2
In this paper, we show that the co-localization of co-Cohen Macaulay modules preserves co-Cohen Macaulayness under a certain condition. In addition, we give a characterization of co-Cohen Macaulay modules by vanishing properties of the dual Bass numbers of modules.
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.
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.
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.
Cominimaxness with respect to ideals of dimension one
Yavar Irani 대한수학회 2017 대한수학회보 Vol.54 No.1
Let $R$ denote a commutative Noetherian (not necessarily local) ring and let $I$ be an ideal of $R$ of dimension one. The main purpose of this note is to show that the category $\mathscr{M}(R, I)_{com}$ of $I$-cominimax $R$-modules forms an Abelian subcategory of the category of all $R$-modules. This assertion is a generalization of the main result of Melkersson in \cite{Me}. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category $\mathcal{C}_{B}^1(R)$ of all $R$-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all $R$-modules.
COMINIMAXNESS WITH RESPECT TO IDEALS OF DIMENSION ONE
Irani, Yavar Korean Mathematical Society 2017 대한수학회보 Vol.54 No.1
Let R denote a commutative Noetherian (not necessarily local) ring and let I be an ideal of R of dimension one. The main purpose of this note is to show that the category ${\mathfrak{M}}(R,\;I)_{com}$ of I-cominimax R-modules forms an Abelian subcategory of the category of all R-modules. This assertion is a generalization of the main result of Melkersson in [15]. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category ${\mathcal{C}}^1_B(R)$ of all R-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all R-modules.