Local-global principle and generalized local cohomology modules
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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 $I$.
Abstract
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 $I$.
참고문헌 (18)
- M. Aghapournahr, "Cofiniteness of weakly Laskerian local cohomology modules", Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 57(105)(4), pp.347~356 (2014)
- D. Asadollahi, "Faltings’ local-global principle for the finiteness of local cohomology modules", Comm. Algebra, 43(3), pp.953~958 (2015)[DOI]
- K. Bahmanpour, "Minimaxness and cofiniteness properties of local cohomology modules", Comm. Algebra, 41(8), pp.2799~2814 (2013)[DOI]
- M. P. Brodmann, "Local cohomology, Cambridge Studies in Advanced Mathematics, 136" (2013), Cambridge Univ. Press
- M. R. Doustimehr, "Faltings’ local-global principle and annihilator theorem for the finiteness dimensions", Comm. Algebra, 47(5), pp.1853~1861 (2019)[DOI]
- G. Faltings, "Der Endlichkeitssatz in der lokalen Kohomologie", Math. Ann, 255(1), pp.45~56 (1981)[DOI]
- A. Fathi, "Local-global principle for the finiteness and Artinianness of generalised local cohomology modules", Bull. Aust. Math. Soc, 87(3), pp.480~492 (2013)[DOI]
- A. Grothendieck, "Cohomologie locale des faisceaux coh´erents et th´eor`emes de Lefschetz locaux et globaux (SGA 2)" (1968), North-Holland
- M. Hatamkhani, "On the local-global principles for the cd local cohomology modules", Algebraic Structures and Their Applications, 8(2), pp.1~15 (2021)
- J. Herzog, "Aufl¨osungen und dualit¨at in der localen Algebra", pp.1970
- N. V. Hoang, "On Faltings’ local-global principle of generalized local cohomology modules", Kodai Math. J, 40(1), pp.58~62 (2017)[DOI]
- H. Matsumura, "Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8" (1986), Cambridge Univ. Press
- S. Rezaei, "S-minimaxness and local cohomology modules", Arch. Math. (Basel), 110(6), pp.563~572 (2018)[DOI]
- H. Roshan-Shekalgourabi, "On the local-global principle for the local cohomology modules", Math. Rep. (Bucur.), 22(2), pp.107~120 (2020)
- Z. M. Tang, "Local-global principle for the Artinianness of local cohomology modules", Comm. Algebra, 40(1), pp.58~63 (2012)[DOI]
- T. Yoshizawa, "Subcategories of extension modules by Serre subcategories", Proc. Amer. Math. Soc, 140(7), pp.2293~2305 (2012)[DOI]
- T. Yoshizawa, "Remarks on the local-global principle for a subcategory consisting extension modules", J. Algebra Appl, 18(12), pp.1950236~1950253 (2019)
- H. Z¨oschinger, "Minimax-moduln", J. Algebra, 102(1), pp.1~32 (1986)[DOI]