ON THE ASSOCIATED PRIME IDEALS OF GENERALIZED d-COHOMOLOGY MODULES

2016 ◽  
Vol 38 (6) ◽  
pp. 561-568
Author(s):  
Mirsadegh Sayedsadeghi
Keyword(s):  
Prime Ideals ◽  
Associated Prime Ideals ◽  
Cohomology Modules ◽  
Associated Prime

On the Finiteness Results of the Generalized Local Cohomology Modules

2009 ◽  
Vol 16 (02) ◽  
pp. 325-332 ◽  
Author(s):  
Amir Mafi
Keyword(s):  
Positive Integer ◽  
Local Cohomology ◽  
Prime Ideals ◽  
Local Cohomology Module ◽  
Local Cohomology Modules ◽  
Associated Prime Ideals ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules ◽  
Infinite Set ◽  
Associated Prime

Let 𝔞 be an ideal of a commutative Noetherian local ring R, and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that if the support of the generalized local cohomology module [Formula: see text] is finite for all i < t, then the set of associated prime ideals of the generalized local cohomology module [Formula: see text] is finite. Also, if the support of the local cohomology module [Formula: see text] is finite for all i < t, then the set [Formula: see text] is finite. Moreover, we prove that gdepth (𝔞+ Ann (M),N) is the least integer t such that the support of the generalized local cohomology module [Formula: see text] is an infinite set.

On the Finiteness Property of Generalized Local Cohomology Modules

2005 ◽  
Vol 12 (02) ◽  
pp. 293-300 ◽  
Author(s):  
K. Khashyarmanesh ◽  
M. Yassi
Keyword(s):  
Local Cohomology ◽  
Prime Ideals ◽  
Local Cohomology Module ◽  
Finiteness Property ◽  
Commutative Noetherian Ring ◽  
Local Cohomology Modules ◽  
Associated Prime Ideals ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules ◽  
Associated Prime

Let [Formula: see text] be an ideal of a commutative Noetherian ring R, and let M and N be finitely generated R-modules. Let [Formula: see text] be the [Formula: see text]-finiteness dimension of N. In this paper, among other things, we show that for each [Formula: see text], (i) the set of associated prime ideals of generalized local cohomology module [Formula: see text] is finite, and (ii) [Formula: see text] is [Formula: see text]-cofinite if and only if [Formula: see text] is so. Moreover, we show that whenever [Formula: see text] is a principal ideal, then [Formula: see text] is [Formula: see text]-cofinite for all n.

scholarly journals Localization at countably infinitely many prime ideals and applications

2016 ◽  
Vol 15 (03) ◽  
pp. 1650045 ◽  
Author(s):  
Kamal Bahmanpour ◽  
Pham Hung Quy
Keyword(s):  
Local Cohomology ◽  
Prime Ideals ◽  
Local Cohomology Modules ◽  
Technical Lemma ◽  
Associated Prime Ideals ◽  
Cohomology Modules ◽  
Associated Prime

In this paper we present a technical lemma about localization at countably infinitely many prime ideals. We apply this lemma to get many results about the finiteness of associated prime ideals of local cohomology modules.

ON THE BEHAVIOR OF APPLYING DERIVED FUNCTORS OF TORSION FUNCTORS ON LOCAL COHOMOLOGY MODULES

2012 ◽  
Vol 11 (06) ◽  
pp. 1250113
Author(s):  
K. KHASHYARMANESH ◽  
F. KHOSH-AHANG
Keyword(s):  
Local Cohomology ◽  
Cohomological Dimension ◽  
Prime Ideals ◽  
Local Cohomology Modules ◽  
Associated Prime Ideals ◽  
Special Cases ◽  
Derived Functors ◽  
Cohomology Modules ◽  
Associated Prime

In this note, by using some properties of the local cohomology functors of weakly Laskerian modules, we study the behavior of right and left derived functors of torsion functors. In fact, firstly we gain some isomorphisms in the context of these functors, grade and cohomological dimension. Then we study their supports and their sets of associated prime ideals in special cases.

A finite result for the set of associated prime ideals of formal local cohomology modules

2018 ◽  
Vol 13 (02) ◽  
pp. 2050046
Author(s):  
Pham Huu Khanh
Keyword(s):  
Maximal Ideal ◽  
Local Cohomology ◽  
Prime Ideals ◽  
Local Cohomology Modules ◽  
Associated Prime Ideals ◽  
Finite Set ◽  
Formal Local Cohomology ◽  
Cohomology Modules ◽  
Associated Prime ◽  
Finite Result

Let [Formula: see text] be a Noetherian local ring, [Formula: see text] two ideals of [Formula: see text], and [Formula: see text] two finitely generated [Formula: see text]-modules. It is first shown that [Formula: see text] is a finite set. We also prove that except the maximal ideal [Formula: see text], the set [Formula: see text] is stable for large [Formula: see text], where we use [Formula: see text] to denote [Formula: see text]-module [Formula: see text] or [Formula: see text] and [Formula: see text] is the eventual value of [Formula: see text].

Associated prime ideals over skew PBW extensions

2020 ◽  
Vol 48 (12) ◽  
pp. 5038-5055
Author(s):  
Arturo Niño ◽  
María Camila Ramírez ◽  
Armando Reyes
Keyword(s):  
Prime Ideals ◽  
Associated Prime Ideals ◽  
Skew Pbw Extensions ◽  
Associated Prime

Asymptotic Behavior of Integral Closures in Modules

2007 ◽  
Vol 14 (03) ◽  
pp. 505-514 ◽  
Author(s):  
R. Naghipour ◽  
P. Schenzel
Keyword(s):  
Asymptotic Behavior ◽  
Integral Closure ◽  
Prime Ideals ◽  
Finitely Generated ◽  
Large N ◽  
Nagata Ring ◽  
Associated Prime Ideals ◽  
Integral Closures ◽  
Definition Of ◽  
Associated Prime

Let R be a commutative Noetherian Nagata ring, let M be a non-zero finitely generated R-module, and let I be an ideal of R such that height MI > 0. In this paper, there is a definition of the integral closure Na for any submodule N of M extending Rees' definition for the case of a domain. As the main results, it is shown that the operation N → Na on the set of submodules N of M is a semi-prime operation, and for any submodule N of M, the sequences Ass R M/(InN)a and Ass R (InM)a/(InN)a(n=1,2,…) of associated prime ideals are increasing and ultimately constant for large n.

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