On the local cohomology of minimax modules
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Let R be a commutative Noetherian ring, a an ideal of R, and M a minimax R-module. We prove that the local cohomology modules [수식](M) are a-cominimax; that is, [수식](R/a,[수식]H_(M)) is minimax for all i and j in the following cases: (a) dim R/a=1; (b) cd(a)=1, where cd is the cohomological dimension of a in R; (c) dim R ≤ 2. In these cases we also prove that the Bass numbers and the Betti numbers of [수식](M) are finite.
Abstract
Let R be a commutative Noetherian ring, a an ideal of R, and M a minimax R-module. We prove that the local cohomology modules [수식](M) are a-cominimax; that is, [수식](R/a,[수식]H_(M)) is minimax for all i and j in the following cases: (a) dim R/a=1; (b) cd(a)=1, where cd is the cohomological dimension of a in R; (c) dim R ≤ 2. In these cases we also prove that the Bass numbers and the Betti numbers of [수식](M) are finite.
참고문헌 (17)
- J. Azami, "Finiteness properties of local cohomology modules for a-minimax modules", Proc. Amer. Math. Soc, 137(2), pp.439~448 (2009)
- K. Bahmanpour, "On the cofiniteness of local cohomology modules", Proc. Amer. Math. Soc, 136(7), pp.2359~2363 (2008)
- K. Bahmanpour, "Cofiniteness of local cohomology modules for ideals of small dimension", J. Algebra, 321(7), pp.1997~2011 (2009)
- R. Belshoff, "The local cohomology modules of Matlis reflexive modules are almost cofinite", Proc. Amer. Math. Soc, 124(9), pp.2649~2654 (1996)
- R. Belshoff, "Finiteness properties for Matlis reflexive modules", Comm. Algebra, 24(4), pp.1371~1376 (1996)
- M. P. Brodmann, "Local Cohomology: an algebraic introduction with geometric applications", Cambridge Studies in Advanced Mathematics, 60 (1998), Cambridge University Press
- D. Delfino, "Cofinite modules and local cohomology", J. Pure Appl. Algebra, 121(1), pp.45~52 (1997)
- E. Enochs, "Flat covers and flat cotorsion modules", Proc. Amer. Math. Soc, 92(2), pp.179~184 (1984)
- A. Grothendieck, "Local Cohomology", Lecture Notes in Math, 862 (1966), Springer-Verlag
- R. Hartshorne, "Affine duality and cofiniteness", Invent. Math, 9, pp.145~164 (1970)
- K. I. Kawasaki, "Cofiniteness of local cohomology modules for principal ideals", Bull. London Math. Soc, 30(3), pp.241~246 (1998)
- K. Khashyarmanesh, "On the local cohomology of Matlis reflexive modules", Comm. Algebra, 36(2), pp.665~669 (2008)
- L. Melkersson, "Modules cofinite with respect to an ideal", J. Algebra, 285(2), pp.649~668 (2005)
- K. I. Yoshida, "Cofiniteness of local cohomology modules for ideals of dimension one", Nagoya Math. J, 147, pp.179~191 (1997)
- T. Zink, "Endlichkeritsbedingungen fur moduln uber einem Noetherschen ring", Math. Nachr, 64, pp.239~252 (1974)
- H. Zoschinger, "Minimax modules", J. Algebra, 102(1), pp.1~32 (1986)
- H. Zoschinger, "Uber die Maximalbedingung fur radikalvolle Untermoduh", Hokkaido Math. J, 17(1), pp.101~116 (1988)