Publications de l’Institut Mathématique, Nouvelle Série Vol. 102[116], pp. 115–120 (2017) 

Cohomological Dimensions With Respect To Sum And Intersection Of IdealsAlireza VahidiDepartment of Mathematics, Payame Noor University (PNU), IranAbstract: Let $R$ be a commutative Noetherian ring with nonzero identity, $\U0001d51e$ and $\U0001d51f$ proper ideals of $R$, $M$ a finitely generated $R$module with finite projective dimension, and $X$ a finitely generated $R$module. We study the cohomological dimensions of $M$ and $X$ with respect to $\U0001d51e+\U0001d51f$ and $\U0001d51e\cap \U0001d51f$. We show that the inequality ${cd}_{\U0001d51e+\U0001d51f}(M,X)\le {cd}_{\U0001d51e}(M,X)+{cd}_{\U0001d51f}\left(X\right)$ holds true and we find an equivalent condition for it to be equality. Keywords: cohomological dimensions; generalized local cohomology modules; local cohomology modules Classification (MSC2000): 13D05; 13D45 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.
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