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RELATIVE PROJECTIVITY AND RELATED RESULTS
Toroghy, H.Ansari Korean Mathematical Society 2004 대한수학회보 Vol.41 No.3
Let R be a commutative Noetherian ring and let M be an Artinian R-module. Let M${\subseteq}$M′ be submodules of M. Suppose F is an R-module which is projective relative to M. Then it is shown that $Att_{R}$($Hom_{A}$ (F,M′) :$Hom_{A}$(F,M) $In^n$), n ${\in}$N and $Att_{R}$($Hom_{A}$(F,M′) :$Hom_{A}$(F,M) In$^n$ $Hom_{A}$(F,M") :$Hom_{A}$(F,M) $In^n$),n ${\in}$ N are ultimately constant.
M-INJECTIVITY AND ASYMPTOTIC BEHAVIOUR
Toroghy, H.-Ansari Korean Mathematical Society 2002 대한수학회보 Vol.39 No.2
Let R be a commutative Noetherian ring and M an R-module. In this paper we will consider the asymptotic behaviour of ideals relative to an R-module E which is M-injective.
ASYMPTOTIC STABILITY OF SOME SEQUENCES RELATED TO INTEGRAL CLOSURE
TOROGHY, H. ANS 호남수학회 2002 한국수학학술지 Vol.24 No.1
In this paper we will show that if E is an injective module over a commutative ring A, then the sequence of sets Ass_A(A/(J^n)^*(E)), n∈N, is increasing and ultimately constant. Also we will obtain some results concerning the integral closure of ideals related to some modules.
ASYMPTOTIC BEHAVIOUR OF IDEALS RELATIVE TO SOME MODULES OVER A COMMUTAYIVE NOETHEILAN RING
TOROGHY, H. ANSARI 호남수학회 2001 한국수학학술지 Vol.23 No.1
Let E be an injective module over a commutative Noetherian ring A. In this paper we will show that if I is a regular ideal, then the sequence of sets Ass_A((I^n)^*(E)/I^n), n∈N is ultimately constant. Also we obtain some related results. (Here for an ideal J of A, J^*(E) denotes the integral closure of J relative to E.
COMULTIPLICATION MODULES AND RELATED RESULTS
Ansari-Toroghy, H.,Farshadifar, F. The Honam Mathematical Society 2008 호남수학학술지 Vol.30 No.1
Let R be a commutative ring (with identity). In this paper we will obtain some results concerning comultiplication R-modules. Further we state and prove a dual notion of Nakayama's lemma for finitely cogenerated modules.
TIGHT CLOSURE OF IDEALS RELATIVE TO MODULES
Ansari-Toroghy, H.,Dorostkar, F. The Honam Mathematical Society 2010 호남수학학술지 Vol.32 No.4
In this paper the dual notion of tight closure of ideals relative to modules is introduced and some related results are obtained.
△-CLOSURES OF IDEALS WITH RESPECT TO MODULES
Ansari-Toroghy, H.,Dorostkar, F. The Honam Mathematical Society 2008 호남수학학술지 Vol.30 No.1
Let M be an arbitrary module over a commutative Noetherian ring R and let ${\triangle}$ be a multiplicatively closed set of non-zero ideals of R. In this paper, we will introduce the dual notion of ${\triangle}$-closure and ${\triangle}$-dependence of an ideal with respect to M and obtain some related results.
ON THE PRIME SPECTRUM OF A MODULE OVER A COMMUTATIVE NOETHERIAN RING
Ansari-Toroghy, H.,Sarmazdeh-Ovlyaee, R. The Honam Mathematical Society 2007 호남수학학술지 Vol.29 No.3
Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $Supp_{R}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.
A Survey of Asymptotic Associated, Attached, and Coassocited Primes Relative to Some Modules
Ansari-Toroghy, H. The Honam Mathematical Society 2003 호남수학학술지 Vol.25 No.1
Recently there has been a large body of interest research on asymptotic behaviour of ideals relative to some modules. The purpose of this paper is to provide a survey of these new results.
ASYMPTOTIC BEHAVIOUR OF IDEALS RELATIVE TO SOME MODULES OVER A COMMUTATIVE NOETHERIAN RING
ANSARI-TOROGHY, H. The Honam Mathematical Society 2001 호남수학학술지 Vol.23 No.1
Let E be an injective module over a commutative Noetherian ring A. In this paper we will show that if I is regular ideal, then the sequence of sets $$Ass_A((I^n)^{{\star}(E)}/I^n),\;n{\in}N$$ is ultimately constant. Also we obtain some related results. (Here for an ideal J of A, $J^{{\star}(E)}$ denotes the integral closure of J relative to E.