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

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Cohomological Dimensions With Respect To Sum And Intersection Of Ideals

Alireza Vahidi

Department of Mathematics, Payame Noor University (PNU), Iran

Abstract: Let R be a commutative Noetherian ring with non-zero identity, 𝔞 and 𝔟 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 𝔞+𝔟 and 𝔞𝔟. We show that the inequality cd 𝔞+𝔟 (M,X)cd 𝔞 (M,X)+cd 𝔟 (X) 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

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Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.

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