Title : ( Some splitting theorems for extension and torsion functors of local cohomology modules )
Authors: Ebrahim Zangoiezadeh , Kazem Khashyarmanesh ,
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Abstract
Let Rbe a commutative ring with identity, a an ideal of Rand Ma finitely generated R-module. In this paper, for fixed integers t and j, we study the existence of the following isomorphisms of local cohomology modules: (i)H_a(M/xM) =H_a(M) ⊕H_a(M); (ii)Ext^jR(Ra, Hta(M/xM)) =ExtjR(Ra, H_a(M)) ⊕Ext^jR(Ra,Ht+1a(M)); and, (iii)Tor_Rj(Ra, Hta(M/xM)) =Tor_Rj(Ra, Ha(M)) ⊕Ra,H_a(M)), for some a-filter regular element x on M. Also, we provide some applications of the above isomorphisms.
Keywords
Local cohomology Split exact sequence Extension functor Torsion functor Filter regular element
@article{paperid:1070608,
author = {Ebrahim Zangoiezadeh and Khashyarmanesh, Kazem},
title = {Some splitting theorems for extension and torsion functors of local cohomology modules},
journal = {Journal of Algebra},
year = {2018},
volume = {503},
number = {1},
month = {June},
issn = {0021-8693},
pages = {329--339},
numpages = {10},
keywords = {Local cohomology
Split exact sequence
Extension functor
Torsion functor
Filter regular element},
}
%0 Journal Article
%T Some splitting theorems for extension and torsion functors of local cohomology modules
%A Ebrahim Zangoiezadeh
%A Khashyarmanesh, Kazem
%J Journal of Algebra
%@ 0021-8693
%D 2018
