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LOCAL-GLOBAL PRINCIPLE AND GENERALIZED LOCAL COHOMOLOGY MODULES
Bui Thi Hong Cam,Nguyen Minh Tri,Do Ngoc Yen Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.3
Let 𝓜 be a stable Serre subcategory of the category of R-modules. We introduce the concept of 𝓜-minimax R-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the 𝓜-minimaxness. We also provide the 𝓜-finiteness dimension f<sup>𝓜</sup><sub>I</sub> (M, N) of M, N relative to I which is an extension the finiteness dimension f<sub>I</sub> (N) of a finitely generated R-module N relative to I.