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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.
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.
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.
ON THE INTEGRAL CLOSURES OF IDEALS
Ansari-Toroghy, H.,Dorostkar, F. The Honam Mathematical Society 2007 호남수학학술지 Vol.29 No.4
Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)
Max<sub>R</sub>(M) AND ZARISKI TOPOLOGY
ANSARI-TOROGHY, H.,KEIVANI, S.,OVLYAEE-SARMAZDEH, R. 호남수학회 2006 호남수학학술지 Vol.28 No.3
Let R be a commutative ring and let M be an R-module. Let X = $Spec_R(M)$ be the prime spectrum of M with Zariski topology. In this paper, by using the topological properties of X, we will obtain some conditions under which $Max_R(M)=Spec_R(M)$.
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.
Tight Closure Of Ideals Relative To Modules
( H Ansari Toroghy ),( F Dorostakar ) 호남수학회 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.