filter regular sequence
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2020 ◽  
Vol 378 (1-2) ◽  
pp. 243-254
Author(s):  
Linquan Ma ◽  
Pham Hung Quy ◽  
Ilya Smirnov


2009 ◽  
Vol 16 (04) ◽  
pp. 653-660
Author(s):  
Kazem Khashyarmanesh

Given a commutative Noetherian local ring (R, 𝔪), it is shown that R is Gorenstein if and only if there exists a system of parameters x1,…,xd of R which generates an irreducible ideal and [Formula: see text] for all t > 0. Let n be an arbitrary non-negative integer. It is also shown that for an arbitrary ideal 𝔞 of a commutative Noetherian (not necessarily local) ring R and a finitely generated R-module M, [Formula: see text] is finitely generated if and only if there exists an 𝔞-filter regular sequence x1,…,xn∈ 𝔞 such that [Formula: see text] for all t > 0.



2009 ◽  
Vol 08 (06) ◽  
pp. 855-862 ◽  
Author(s):  
ALI AKBAR MEHRVARZ ◽  
KAMAL BAHMANPOUR ◽  
REZA NAGHIPOUR

Let I be an ideal of a commutative Noetherian ring R such that ara (I) = t ≥ 2. The purpose of this article is to show that there exists an I-filter regular sequence y1, …, yt for R such that Rad (I) = Rad (y1, …, yt) and cd ((y1, …, yi), R) = i for all 1 ≤ i < t. Also, it is shown that ara (I) ≤ dim R + 1, which is a generalization of a nice result of Kronecker [14]. In addition, some applications are included.



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