On the Matlis duals of local cohomology modules and modules of generalized fractions
Year
: 2010
Abstract: Let (R,m) be a commutative Noetherian local ring with
non-zero identity, a a proper ideal of R and M a finitely
generated R-module with a M\\\\neq M. Let
D(-):=Hom_R(-,E) be the Matlis dual functor, where
E:=E(R/m) is the injective hull of the residue field R/m.
In this paper, by using a complex which involves modules of
generalized fractions, we show that, if x_1, ... ,x_n is a
regular sequence on
M contained in a, then H^n_(x_1, ... ,x_n)R
(D(H^n_a(M))) is a homomorphic image of D(M), where H^i_b(-) is
the i-th local cohomology functor with respect to an ideal
b of R. By applying this result, we study some conditions on
a certain module of generalized fractions under which
D(H^n_(x_1,... ,x_n)(D(H^n_a(M))))\\\\cong D(D(M)).
non-zero identity, a a proper ideal of R and M a finitely
generated R-module with a M\\\\neq M. Let
D(-):=Hom_R(-,E) be the Matlis dual functor, where
E:=E(R/m) is the injective hull of the residue field R/m.
In this paper, by using a complex which involves modules of
generalized fractions, we show that, if x_1, ... ,x_n is a
regular sequence on
M contained in a, then H^n_(x_1, ... ,x_n)R
(D(H^n_a(M))) is a homomorphic image of D(M), where H^i_b(-) is
the i-th local cohomology functor with respect to an ideal
b of R. By applying this result, we study some conditions on
a certain module of generalized fractions under which
D(H^n_(x_1,... ,x_n)(D(H^n_a(M))))\\\\cong D(D(M)).
Keyword(s): local cohomology module,Matlis dual functor,module of generalized fractions,filter regular sequence
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On the Matlis duals of local cohomology modules and modules of generalized fractions
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| contributor author | کاظم خشیارمنش | en |
| contributor author | Kazem Khashyarmanesh | fa |
| date accessioned | 2020-06-06T14:24:24Z | |
| date available | 2020-06-06T14:24:24Z | |
| date issued | 2010 | |
| identifier uri | https://libsearch.um.ac.ir:443/fum/handle/fum/3395329?locale-attribute=en | |
| description abstract | Let (R,m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with a M\\\\neq M. Let D(-):=Hom_R(-,E) be the Matlis dual functor, where E:=E(R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x_1, ... ,x_n is a regular sequence on M contained in a, then H^n_(x_1, ... ,x_n)R (D(H^n_a(M))) is a homomorphic image of D(M), where H^i_b(-) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D(H^n_(x_1,... ,x_n)(D(H^n_a(M))))\\\\cong D(D(M)). | en |
| language | English | |
| title | On the Matlis duals of local cohomology modules and modules of generalized fractions | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | local cohomology module | en |
| subject keywords | Matlis dual functor | en |
| subject keywords | module of generalized fractions | en |
| subject keywords | filter regular sequence | en |
| journal title | Proceedings of the Indian Academy of Sciences - Mathematical Sciences | fa |
| pages | 35-43 | |
| journal volume | 120 | |
| journal issue | 1 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1015209.html | |
| identifier articleid | 1015209 |