Some results on top local cohomology and top formal local cohomology modules

2016 ◽  
Vol 45 (5) ◽  
pp. 1935-1940
Author(s):  
Shahram Rezaei
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Formal Local Cohomology ◽  
Cohomology Modules

Artinianness and Attached Primes of Formal Local Cohomology Modules

2014 ◽  
Vol 21 (02) ◽  
pp. 307-316 ◽  
Author(s):  
Mohammad Hasan Bijan-Zadeh ◽  
Shahram Rezaei
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Upper Bounds ◽  
Finitely Generated ◽  
Lower And Upper Bounds ◽  
Local Cohomology Modules ◽  
Formal Local Cohomology ◽  
Cohomology Modules

Let 𝔞 be an ideal of a local ring (R, 𝔪) and M a finitely generated R-module. In this paper we study the Artinianness properties of formal local cohomology modules and we obtain the lower and upper bounds for Artinianness of formal local cohomology modules. Additionally, we determine the set [Formula: see text] and we show that the set of all non-isomorphic formal local cohomology modules [Formula: see text] is finite.

scholarly journals General formal local cohomology modules

2020 ◽  
Vol 30 (2) ◽  
pp. 254-266
Author(s):  
Sh. Rezaei ◽  
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Finitely Generated ◽  
Local Cohomology Module ◽  
Local Cohomology Modules ◽  
Formal Local Cohomology ◽  
Cohomology Modules

Let (R,m) be a local ring, Φ a system of ideals of R and M a finitely generated R-module. In this paper, we define and study general formal local cohomology modules. We denote the ith general formal local cohomology module M with respect to Φ by FiΦ(M) and we investigate some finiteness and Artinianness properties of general formal local cohomology modules.

scholarly journals On Artinianness of Formal Local Cohomology, Colocalization and Coassociated Primes

2013 ◽  
Vol 113 (1) ◽  
pp. 5 ◽  
Author(s):  
Majid Eghbali
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Formal Local Cohomology ◽  
Cohomology Modules

This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.

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].

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