Title : ( Filter regular sequences and endomorphisms of local cohomology modules )
Authors: Ebrahim Zangoiezadeh , Kazem Khashyarmanesh ,
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Abstract
Let R be a commutative Noetherian ring and a be an ideal of R such that cd(a,R) − grade(a,R) ≤ 1, where cd(a,R) is the cohomological dimension of R with respect to a and grade(a,R) is the grade of a. We show that whenever, Exti R(Rz,R) = 0 =Ext_jR(Rz,Hn−1 a (R)) for all z ∈ a and all integers i, j with i > 0 and j ≥ 0, then there exists an exact sequence 0 → Extn R(Hna (R), R) → EndR(Hna (R)) → EndR(Hn−1a (R)) → Extn+1R (Hn a (R), R)of endomorphisms of local cohomology modules, where n := cd(a,R) and, for z ∈ R, Rz is the ring of fractions of R with respect to multiplicatively closed subset {zj | j ≥ 0} of R.
Keywords
Local cohomology module; endomorphism ring; ˇ Cech complex; regular sequence; filter regular sequence.
@article{paperid:1070612,
author = {Ebrahim Zangoiezadeh and Khashyarmanesh, Kazem},
title = {Filter regular sequences and endomorphisms of local cohomology modules},
journal = {Journal of Algebra and its Applications},
year = {2017},
volume = {17},
number = {11},
month = {October},
issn = {0219-4988},
pages = {1850213--18502138},
numpages = {16651925},
keywords = {Local cohomology module; endomorphism ring; ˇ Cech complex; regular
sequence; filter regular sequence.},
}
%0 Journal Article
%T Filter regular sequences and endomorphisms of local cohomology modules
%A Ebrahim Zangoiezadeh
%A Khashyarmanesh, Kazem
%J Journal of Algebra and its Applications
%@ 0219-4988
%D 2017
