The local cohomology theory plays an important role in commutative algebra and algebraic geometry. The I-cofiniteness of local cohomology modules is one of interesting properties which has been studied by many mathematicians. The I-cominimax modules is an extension of I-cofinite modules which was introduced by Hartshorne. An R-module M is I-cominimax if Supp_R(M)\subseteq V(I) and Ext^i_R(R/I,M) is minimax for allÂ i\ge 0. In this paper, we show some conditions such that the generalized local cohomology module H^i_I(M,N) is I-cominimax for all i\ge 0. We show that if H^i_I(M,K) is I-cofinite for all i<t and all finitely generated R-module K, thenÂ H^i_I(M,N) is I-cominimax for all i<tÂ and all minimax R-module N.Â If M is a finitely generated R-module, N is a minimax R-module and t is a non-negative integer such thatÂ dim Supp_R(H^i_I(M,N))\le 1 for all i<t then H^i_I(M,N) is I-cominimax for allÂ i<t. WhenÂ dim R/I\le 1 and H^i_I(N) is I-cominimax for allÂ i\ge 0 then H^i_I(M,N) is I-cominimax for all i\ge 0.
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How to Cite
Bui, C., & Nguyen, T. (2020). On the cominimaxness of generalized local cohomology modules. Science and Technology Development Journal, 23(1), 479-483. https://doi.org/https://doi.org/10.32508/stdj.v23i1.1696
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Science and Technology Development Journal (STDJ) (1859-0128) is the official journal of Viet Nam National University Ho Chi Minh City, Viet Nam, published by Viet Nam National University Ho Chi Minh City, Viet Nam. Science & Technology Development Journal is a multiple discipline science journal covering from natural science, engineering & technology, humanities, art, laws, economics, earth science, environment, social sciences and health sciences.