We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Cofiniteness with respect to a Serre subcategory.
- Authors
Hajikarimi, A.
- Abstract
Let Φ be a system of ideals in a commutative Noetherian ring R, and let [InlineMediaObject not available: see fulltext.] be a Serre subcategory of R-modules. We set . Suppose that a is an ideal of R, and M and N are two R-modules such that M is finitely generated and N ∈ [InlineMediaObject not available: see fulltext.]. It is shown that if the functor $$ D_\Phi ( \cdot ) = \mathop {\lim }\limits_{\overrightarrow {\mathfrak{b} \in \Phi } } Hom_R (\mathfrak{b}, \cdot ) $$ is exact, then, for any $$ \mathfrak{b} \in \Phi ,Ext_R^j (R/\mathfrak{b},H_\Phi ^i (M,N)) $$ ∈ [InlineMediaObject not available: see fulltext.] for all i, j ≥ 0. It is also proved that if there is a nonnegative integer t such that $$ H_\mathfrak{a}^i (M,N) $$ ∈ [InlineMediaObject not available: see fulltext.] for all i < t, then $$ Hom_R (R/\mathfrak{a},H_\mathfrak{a}^t (M,N)) $$ ∈ [InlineMediaObject not available: see fulltext.], provided that [InlineMediaObject not available: see fulltext.] is contained in the class of weakly Laskerian R-modules. Finally, it is shown that if L is an R-module and t is the infimum of the integers i such that $$ H_\mathfrak{a}^i (L) $$ ∈ [InlineMediaObject not available: see fulltext.], then $$ Ext_R^j (R/\mathfrak{a},H_\mathfrak{a}^t (M,L)) $$ ∈ [InlineMediaObject not available: see fulltext.] if and only if $$ Ext_R^j (R/\mathfrak{a},Hom_R (M,H_\mathfrak{a}^t (L))) $$ ∈ [InlineMediaObject not available: see fulltext.] for all j ≥ 0.
- Subjects
FINITE groups; GROUP theory; NOETHERIAN rings; COMMUTATIVE rings; RING theory
- Publication
Mathematical Notes, 2011, Vol 89, Issue 1/2, p121
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434611010135