• 한국자기학회:학술대회 개요집
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• 한국자기학회 2008년도 Asian Magnetics Conference
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• pp.4.2-4.2
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• 2008

• 대한수학회지
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• 제58권6호
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• pp.1513-1528
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• 2021

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map 𝜙 : R → R_Nil(R) by ${\phi}(r)=\frac{r}{1}$ for r ∈ R and 𝜓 : M → M_Nil(R) by ${\psi}(x)=\frac{x}{1}$ for x ∈ M. Then 𝜓(M) is a 𝜙(R)-module. An R-module P is said to be 𝜙-projective if 𝜓(P) is projective as a 𝜙(R)-module. In this paper, 𝜙-exact sequences and 𝜙-projective R-modules are introduced and the rings over which all R-modules are 𝜙-projective are investigated.

• 호남수학학술지
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• 제23권1호
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• pp.15-20
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• 2001

Reduced Von Neumann Regular ring is pseudo symmetric and N(R) is reduced. Thus N(R) is pseudo symmetric and M(R) is reduced if and only if M(R) = N(R).

• Korean Journal of Mathematics
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• 제18권3호
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• pp.261-269
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• 2010

We introduce the concept of fuzzy co-$r$-M-semicontinuous, and investigate the relationships between fuzzy co-$r$-M-semicontinuous mappings and several types of fuzzy $r$-minimal semicompactness.

• East Asian mathematical journal
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• 제25권4호
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• pp.441-447
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• 2009

Jat and Choudhari defined a near-ring R with left bipotent or right bipotent condition in 1979. Also, we can dene a near-ring R as subcommutative if aR = Ra for all a in R. From these above two concepts it is natural to investigate the near-ring R with the properties aR = $Ra^2$ (resp. $a^2R$ = Ra) for each a in R. We will say that such is a near-ring with (1,2)-potent condition (resp. a near-ring with (2,1)-potent condition). Thus, we can extend a general concept of a near-ring R with (m,n)-potent condition, that is, $a^mR\;=\;Ra^n$ for each a in R, where m, n are positive integers. We will derive properties of near-ring with (1,n) and (n,1)-potent conditions where n is a positive integer, any homomorphic image of (m,n)-potent near-ring is also (m,n)-potent, and we will obtain some characterization of regular near-rings with (m,n)-potent conditions.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.607-617
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• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.653-662
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• 2005

In this paper we shall give the relationships among $T_R,\;End_{R}(M),\;SEnd_{R}(M)\;and\;SAut_R(M)$ when M is a perfect R-module. If M and N are perfect modules, we get $SAut_{R}(M {\times}N){\cong}SAut_{R}(M){\times}SAut_R(N)$. Also we shall discuss that $_x(M)_H$ is a subgroup of $_x(M)$ if M is quasi-perfect and $_x(M)_H$ is a normal subgroup of $_x(M)$ if M is perfect.

• 대한수학회지
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• 제51권2호
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• pp.239-250
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• 2014

Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim$_RH_I^i(M){\leq}k$ for ${\forall}i$ < t, then $$\displaystyle\bigcup_{i=0}^{j}(Ass_RH_I^i(M))_{{\geq}k}=\displaystyle\bigcup_{i=0}^{j}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$$ for ${\forall}j{\leq}t$ and ${\forall}n$ >0. This shows that${\bigcup}_{n>0}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$ is a finite set for ${\forall}i{\leq}t$. Also, we prove that $\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1^{n_1},x_2^{n_2},{\ldots},x_i^{n_i})M)_{{\geq}k}=\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1,x_2,{\ldots},x_i)M)_{{\geq}k}$ if $x_1,x_2,{\ldots},x_r$ is M-sequences in dimension > k and $n_1,n_2,{\ldots},n_r$ are some positive integers. Here, for a subset T of Spec(R), set $T_{{\geq}i}=\{{p{\in}T{\mid}dimR/p{\geq}i}\}$.

• 대한수학회보
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• 제57권5호
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• pp.1165-1176
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• 2020

Let M be a module over a commutative ring R. In this paper, we study Int(R, M), the module of integer-valued polynomials on M over R, and Int_M(R), the ring of integer-valued polynomials on R over M. We establish some properties of Krull dimensions of Int(R, M) and Int_M(R). We also determine when Int(R, M) and Int_M(R) are nontrivial. Among the other results, it is shown that Int(ℤ, M) is not Noetherian module over Int_M(ℤ) ∩ Int(ℤ), where M is a finitely generated ℤ-module.

• 대한수학회보
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• 제51권2호
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• pp.373-386
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• 2014

Let (R,m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth($M/I^nM$) = d for $n{\gg}0$. Also we show that, if dim(R) = d and $I_1{\subset}\;{\cdots}\;{\subset}I_n$ is a chain of ideals of R such that $R/I_k$ is maximal Cohen-Macaulay for all k, then $n{\leq}{\ell}_R(R/(a_1,{\ldots},a_d)R)$ for every system of parameters $a1,{\ldots},a_d$ of R. Also, in the case where dim(R) = 2, we prove that the ideal transform $D_m(R/p)$ is minimax balanced big Cohen-Macaulay, for every $p{\in}Assh_R$(R), and we give some equivalent conditions for this ideal transform being maximal Cohen-Macaulay.