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- 저자 : Waqas Mahmood (검색결과 2 건)
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A note on endomorphisms of local cohomology modules
Waqas Mahmood,Zohaib Zahid 대한수학회 2017 대한수학회보 Vol.54 No.1
Let $I$ denote an ideal of a Noetherian local ring $(R,\mathfrak{m})$. Let $M$ denote a finitely generated $R$-module. We study the endomorphism ring of the local cohomology module $H^c_I(M), c = \grade (I,M)$. In particular there is a natural homomorphism $$\Hom_{\hat{R}^I}(\hat{M}^I, \hat{M}^I)\to \Hom_{R}(H^c_{I}(M),H^c_{I}(M)),$$ where $\hat{\cdot}^I$ denotes the $I$-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J \subset I$ with the property $\grade(I,M) = \grade(J,M)$. Our results extends constructions known in the case of $M = R$ (see e.g.~\cite{h1}, \cite{p7}, \cite{p1}).
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A NOTE ON ENDOMORPHISMS OF LOCAL COHOMOLOGY MODULES
Mahmood, Waqas,Zahid, Zohaib Korean Mathematical Society 2017 대한수학회보 Vol.54 No.1
Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).
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