Communications of the
Korean Mathematical Society CKMS

Let $\mathcal{M}$ be a stable Serre subcategory of the category of $R$-modules. We introduce the concept of $\mathcal{M}$-minimax $R$-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the $\mathcal{M}$-minimaxness. We also provide the $\mathcal{M}$-finiteness dimension $f^{\mathcal{M}}_I(M,N)$ of $M,N$ relative to $I$ which is an extension the finiteness dimension $f_I(N)$ of a finitely generated $R$-module $N$ relative to $I$.

Keywords: Finiteness dimension, generalized local cohomology, local-global principle, Serre subcategories

MSC numbers: Primary 13D45, 13C60

Supported by: This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number C2023-26-15.