• East Asian mathematical journal
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• v.16 no.1
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• pp.33-48
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• 2000

In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

• Journal of the Korean Geographical Society
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• v.52 no.1
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• pp.73-103
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• 2017

This paper reports the distribution of soil piles set up during the Yimjin(1712) Boundary Making and Demarcation(YBMD). Through the survey on the distribution of soil piles the location of 'Suchul'(水出: seepage zone) could be identified. The endpoint soil pile set up on the east-south bank of Heishigou(黑石溝) stream locates on $42^{\circ}04^{\prime}20.09^{{\prime}{\prime}}N$, $128^{\circ}16^{\prime}08.42^{{\prime}{\prime}}E$. The west beginning point of soil piles distributed in the south side of Tuhexian road locates on $42^{\circ}02^{\prime}20.14^{{\prime}{\prime}}N$, $128^{\circ}18^{\prime}53.40^{{\prime}{\prime}}E$. And the east endpoint of them locates $42^{\circ}01^{\prime}32.97^{{\prime}{\prime}}N$, $128^{\circ}21^{\prime}24.59^{{\prime}{\prime}}E$. From the west beginning point to the soil pile located in 2.1km distance from the beginning point, the distribution direction is west-east. The direction of soil piles after them is northwest-southeast. The total real length of soil piles distributed in the south side of Tuhexian(圖和線) road is about 4.2km more or less. The location of 'Suchul' written on the Mukedeng's map locates on $42^{\circ}01^{\prime}30.36^{{\prime}{\prime}}N$, $128^{\circ}21^{\prime}3.62^{{\prime}{\prime}}E$, The point locates in southeastward 222m distance from the soil piles endpoint of the south side of Tuhexian road. In reference of these reports this paper develops some reinterpretation on the YBMD.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.135-139
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• 1997

We introduce the concepts of weakly prime and weakly semi-prime ideals in po-${\Gamma}$-semigroup and give some characterizations of weakly prime and weakly semi-prime ideals of po-${\Gamma}$-semigroups analogous to the characterizations of weakly prime and weakly semi-prime ideals of po-semigroups considered by N. Kehayopulu.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.679-686
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• 2010

This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,\;u(t),\;u^{\prime\prime}(t))$, $0\;{\leq}\;t\;{\leq}1$, ${\alpha}u(0)-{\beta}u^{\prime}(0)={\gamma}u(1)+{\delta}u^{\prime}(1)=0$, $au^{\prime\prime}(\xi_1)-bu^{\prime\prime\prime}(\xi_1)=cu^{\prime\prime}(\xi_2)+du^{\prime\prime\prime}(\xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.987-1030
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• 2001

Some discrimination of modules whose endomorhism rings are prime is introduced, by means of structures of submodules inducing prime ideals of the endomorphism ring End(sub)R (M) of a left R-module (sub)RM over a ring R. Modules with non-prime endomorphism rings are contrapositively studied as well.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1271-1290
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• 2013

Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, it coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the general theory are M-$m$-system sets, M-$n$-system sets, M-prime radical and M-Baer's lower nilradical of modules. Relationships between these concepts and basic properties are established. In particular, we identify certain submodules of M, called "primeM-ideals", that play a role analogous to that of prime (two-sided) ideals in the ring R. Using this definition, we show that if M satisfies condition H (defined later) and $Hom_R(M,X){\neq}0$ for all modules X in the category ${\sigma}[M]$, then there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules in ${\sigma}[M]$ and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime submodules and M-prime radical of Artinian modules.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.305-320
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• 2021

In this paper, the relations between L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of a poset and L-fuzzy semi-prime (respectively, L-fuzzy prime) ideals of the lattice of all ideals of a poset are established. A result analogous to Separation Theorem is obtained using L-fuzzy semi-prime ideals.

• Korean Journal of Microbiology
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• v.19 no.3
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• pp.103-107
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• 1981

Increasing the concentration of the nonionic surfactants the solubility of methyl paraben was increased. This is called the solubilization phenomenon and caused inactivation of the preservatives used. The MICs(minimum inhibitory concentrations) on E. coli were increased at the same time. So the relation between the solubility and the mic could be expressed as $S-S_0=R^{\prime}/R^{\prime\prime}\;(M-M_0)$ and in this case $R^{\prime}/R^{\prime\prime}$ was about 2.

• Bulletin of the Korean Chemical Society
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• v.16 no.1
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• pp.1-2
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.9-16
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• 2006

The purpose of this paper is to define the symmetric $bi-(\sigma,\;\tau)$ derivations on prime and semi prime Gamma rings and to prove some results concerning symmetric $bi-(\sigma,\;\tau)$derivations on prime and semi prime Gamma rings.