Wyniki wyszukiwania

1

Associated primes, integral closures and ideal topologies

100%

Naghipour R.

Colloquium Mathematicum

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2006

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tom 105

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nr 1

35-43

EN

Let 𝔞 ⊆ 𝔟 be ideals of a Noetherian ring R, and let N be a non-zero finitely generated R-module. The set Q̅*(𝔞,N) of quintasymptotic primes of 𝔞 with respect to N was originally introduced by McAdam. Also, it has been shown by Naghipour and Schenzel that the set $A*_{a}(𝔟,N) := ⋃ _{n≥1} Ass_{R}R/(𝔟ⁿ)^{(N)}_{a}$ of associated primes is finite. The purpose of this paper is to show that the topology on N defined by ${(𝔞ⁿ)_{a}^{(N)}:_{R} ⟨𝔟⟩}_{n≥1}$ is finer than the topology defined by ${(𝔟ⁿ)_{a}^{(N)}}_{n≥1}$ if and only if $A*_{a}(𝔟,N)$ is disjoint from the quintasymptotic primes of 𝔞 with respect to N. Moreover, we show that if 𝔞 is generated by an asymptotic sequence on N, then $A*_{a}(𝔞,N) = Q̅*(𝔞,N)$.

2

Associated primes and primal decomposition of modules over commutative rings

63%

Khojali A., Naghipour R.

Colloquium Mathematicum

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2009

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tom 114

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nr 2

191-202

EN

Let R be a commutative ring and let M be an R-module. The aim of this paper is to establish an efficient decomposition of a proper submodule N of M as an intersection of primal submodules. We prove the existence of a canonical primal decomposition, $N = ⋂_{𝔭} N_{(𝔭)}$, where the intersection is taken over the isolated components $N_{(𝔭)}$ of N that are primal submodules having distinct and incomparable adjoint prime ideals 𝔭. Using this decomposition, we prove that for 𝔭 ∈ Supp(M/N), the submodule N is an intersection of 𝔭-primal submodules if and only if the elements of R∖𝔭 are prime to N. Also, it is shown that M is an arithmetical R-module if and only if every primal submodule of M is irreducible. Finally, we determine conditions for the canonical primal decomposition to be irredundant or residually maximal, and for the unique decomposition of N as an irredundant intersection of isolated components.

3

Cofiniteness of torsion functors of cofinite modules

51%

Naghipour R., Bahmanpour K., Gorji I.

Colloquium Mathematicum

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2014

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tom 136

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nr 2

221-230

EN

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely generated R-module. It is shown that the R-modules $Tor_{i}^{R}(N,M)$ are I-cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 1 or dim Supp(N) ≤ 2. This immediately implies that if I has dimension one (i.e., dim R/I = 1) then the R-modules $Tor_{i}^{R}(N,H^{j}_{I}(M))$ are I-cofinite for all i,j ≥ 0. Also, we prove that if R is local, then the R-modules $Tor_{i}^{R}(N,M)$ are I-weakly cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 2 or dim Supp(N) ≤ 3. Finally, it is shown that the R-modules $Tor_{i}^{R}(N,H^{j}_{I}(M))$ are I-weakly cofinite for all i,j ≥ 0 whenever dim R/I ≤ 2.

4

Cohomological dimension filtration and annihilators of top local cohomology modules

51%

Atazadeh A., Sedghi M., Naghipour R.

Colloquium Mathematicum

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2015

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tom 139

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nr 1

25-35

EN

Let 𝔞 denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration $𝓜 = {M_i}_{i = 0}^{c}$, where c = cd(𝔞,M) and $M_i$ denotes the largest submodule of M such that $cd(𝔞,M_i) ≤ i$. Some properties of this filtration are investigated. In particular, if (R,𝔪) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module $H_{𝔞}^{c}(M)$, namely $Ann_{R}(H_{𝔞}^{c}(M)) = Ann_{R}(M/M_{c-1})$. As a consequence, there exists an ideal 𝔟 of R such that $Ann_{R}(H_{𝔞}^{c}(M)) = Ann_{R}(M/H⁰_{𝔟}(M))$. This generalizes the main results of Bahmanpour et al. (2012) and Lynch (2012).

Ograniczanie wyników

4 Colloquium Mathematicum

4 Naghipour R.

1 Atazadeh A.

1 Bahmanpour K.

1 Gorji I.

1 Khojali A.

1 Sedghi M.

1 2015

1 2014

1 2009

1 2006

Associated primes, integral closures and ideal topologies

Associated primes and primal decomposition of modules over commutative rings

Cofiniteness of torsion functors of cofinite modules

Cohomological dimension filtration and annihilators of top local cohomology modules