• East Asian mathematical journal
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• 제16권1호
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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.

• 대한지리학회지
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• 제52권1호
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• pp.73-103
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• 2017

이 논문은 현존하는 임진정계 경계표지 토퇴들의 분포와 특징에 대해 보고하고 있다. 그를 통해 목극등 지도에 표시된 '수출(水出)'의 위치를 확인하고자 하였다. 흑석구 동남안을 따라 설치된 토퇴들 중 마지막 토퇴의 위치는 대략 북위 $42^{\circ}04^{\prime}20.09^{{\prime}{\prime}}$, 동경 $128^{\circ}16^{\prime}08.42^{{\prime}{\prime}}$이다. '도화선 도로변 토퇴군'의 서쪽 시점은 대략 북위 $42^{\circ}02^{\prime}20.14^{{\prime}{\prime}}$, 동경 $128^{\circ}18^{\prime}53.40^{{\prime}{\prime}}$이며, 동쪽 종점의 좌표는 대략 북위 $42^{\circ}01^{\prime}32.97^{{\prime}{\prime}}$, 동경 $128^{\circ}21^{\prime}24.59^{{\prime}{\prime}}$이다. 서쪽 시점에서 약 2.1㎞ 지점까지는 대체적으로 "서-동"의 방향이며, 그 이동은 대체적으로 "서북-동남" 방향이다. 도화선 도로변 토퇴의 총 분포 길이는 실제거리 약 4.2㎞ 정도이다. 목극등 지도에 표시된 '수출'의 좌표는 대략 북위 $42^{\circ}01^{\prime}30.36^{{\prime}{\prime}}$, 동경 $128^{\circ}21^{\prime}3.62^{{\prime}{\prime}}$이다. 동쪽 마지막 토퇴의 동남 방향 지도상 평면 직선거리 약 222m 지점이다. 이러한 결과를 근거로 임진정계에 대한 재해석을 시도하였다.

• Korean Journal of Mathematics
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• 제5권2호
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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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• 제28권3_4호
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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.

• 대한수학회지
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• 제38권5호
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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.

• 대한수학회지
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• 제50권6호
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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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• 제29권2호
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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.

• 미생물학회지
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• 제19권3호
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• pp.103-107
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• 1981

1 계면활성제의 농도가 증가하면 용해도와 최소억제농도는 일정하게 증가한다. 2 계연활성제에 결합되어 있는 지방산의 탄소수가 증가하면 용해도와 최소억제농도는 증가한다. 3 용해도와 최소억제농도와의 관계는 $S-S_0=R^{\prime}/R^{\prime\prime}\;(M-M_0)$로써, 본 실험에서 $R^{\prime}/R^{\prime\prime}$는 대략 2가 되었다.

• Bulletin of the Korean Chemical Society
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• 제16권1호
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• pp.1-2
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• 1995

• 대한수학회보
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• 제43권1호
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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.