- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 On the cohomological dimension of finitely generated modules Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 311-317 https://doi.org/10.4134/BKMS.b161017Published online January 1, 2018 Kamal Bahmanpour, Masoud Seidali Samani Institute for Research in Fundamental Sciences (IPM), University of Mohaghegh Ardabili Abstract : Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring and $I$ be an ideal of $R$. In this paper it is shown that if ${\rm cd}(I,R)=t>0$ and the $R$-module $Hom_R(R/I, H^t_I(R))$ is finitely generated, then \begin{align}t={\rm sup}\,\{\dim \widehat{\widehat{R}_{\mathfrak P}}/\mathfrak Q:~&\mathfrak P\in V(I\widehat{R}),\,\,\mathfrak Q\in \rm{mAss}_{\widehat{\widehat{R}_{\mathfrak P}}}\widehat{\widehat{R}_{\mathfrak P}}\,\, \rm{ and}\\ &\mathfrak P\widehat{\widehat{R}_{\mathfrak P}}=\rm{Rad}(I\widehat{\widehat{R}_{\mathfrak P}}+\mathfrak Q)\}.\end{align} Moreover, some other results concerning the cohomological dimension of ideals with respect to the rings extension $R\subset R[X]$ will be included. Keywords : attached prime, cofinite module, cohomological dimension, local cohomology, Noetherian ring MSC numbers : 13D45, 14B15, 13E05 Downloads: Full-text PDF