• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.251-258
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• 2002

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.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.101-113
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• 2008

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.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.53-72
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• 2003

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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.419-426
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• 2004

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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.149-160
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• 2023

Let 𝖆 and 𝖇 be ideals of a commutative Noetherian ring R and M a finitely generated R-module of finite dimension d > 0. In this paper, we obtain some results about the annihilators and attached primes of top local cohomology and top formal local cohomology modules. In particular, we determine Ann(𝖇 H^d_𝖆(M)), Att(𝖇 H^d_𝖆(M)), Ann(𝖇𝔉^d_𝖆(M)) and Att(𝖇𝔉^d_𝖆(M)).

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.531-540
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• 2015

Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all $t{\leq}r$ the sets $$(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/I^n,A)))_{{\geq}k}\;and\\(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/(a_1^{n_1},{\cdots},a_l^{n_l}),A)))_{{\geq}k}$$ are independent of the choice of $n,n_1,{\cdots},n_l$ for any system of generators ($a_1,{\cdots},a_l$) of I.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.737-743
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• 2016

Let a and b be two ideals of a commutative Noetherian ring R, M a finitely generated R-module and i an integer. In this paper we study formal local cohomology modules with respect to a pair of ideals. We denote the i-th a-formal local cohomology module M with respect to b by ${\mathfrak{F}}^i_{a,b}(M)$. We show that if ${\mathfrak{F}}^i_{a,b}(M)$ is artinian, then $a{\subseteq}{\sqrt{(0:{\mathfrak{F}}^i_{a,b}(M))$. Also, we show that ${\mathfrak{F}}^{\text{dim }M}_{a,b}(M)$ is artinian and we determine the set $Att_R\;{\mathfrak{F}}^{\text{dim }M}_{a,b}(M)$.

• Korean Journal of Culture and Social Issue
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• v.14 no.1
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• pp.101-123
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• 2008

We investigated the implicit representations of success/failure associated with mother in male and female college students. In study 1, participants were presented 'mother' or 'basket' as a context prime and 'success' or 'failure' related words as second primes for 100ms, and were asked to make lexical decisions about 'accept' or 'reject' related words and non-words after 150 ms (SOA 250ms). Results revealed that lexical decision times on the mother condition were more rapid than the ones on the basket condition, and lexical decision times on the acceptance condition were more rapid than the ones on the rejection condition, and female participants showed shorter times than male students did. In study 2, we divided participants into four groups by gender and attachment style, Results showed that the interaction between success/failure and acceptance/rejection was statistically significant, that is, quickest lexical decision times on the success-acceptance condition, and slowed times on failure-acceptance, failure-rejection, and success-rejection condition in order. On the other hand, no significant differences between high and low attachment group were found in males, but significant three-way interactions were found in females. In highly attached females, lexical decision times in success-acceptance condition were not differed from ones in success-rejection condition, and slowed times in failure-rejection condition. Low attached females showed very rapid times in success-acceptance condition, but very slow times in success-rejection condition. The results were discussed in terms of self-positivity and success/failure scheme depending on gender and attachment styles.