• 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.

• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.233-242
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• 2004

The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $\Gamma$-ring and Q a quotient $\Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $W\Gamma$W $\neq 0. Furthermore Q is a semi-prime $\Gamma$-ring. (2) Let M be a semi-prime $\Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{\Gamma}$ is a regular $\Gamma$-ring. (3) Let M be a semi-prime $\Gamma$-ring and $C_{\gamma}$ the extended centroid of M. If $C_{\gamma}$ is a $\Gamma$-field, then the $\Gamma$-ring M is a prime $\Gamma$-ring.

• 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.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.385-402
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• 2015

In this paper we study the (good) semi-prime closure operations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover by given some examples we show that the given different notions are independent together, for instance there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of "$c_f$-Max X", we prove that every member of "$c_f$-Max X" is a prime ideal. Also we conclude some more related results.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.603-612
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• 2012

In this paper, we introduce and study the intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideals of ${\Gamma}$-LA-semigroups and some interesting properties are investigated. The main result of the paper is: if $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an IFS in ${\Gamma}$-LA-semigroup S, then $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideal of S if and only if for any $s,t{\in}[0,1]$, the sets $U({\mu}_A,s)=\{x{\in}S:{\mu}_A(x){\geq}s\}$ and $L({\gamma}_A,t)=\{x{\in}S:{\gamma}_A(x){\leq}t\}$ are prime (semi-prime) ${\Gamma}$-ideals of S.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.203-213
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• 2007

The aim of this paper is to introduce modules over the generalized of a semi-prime ${\Gamma}$-ring

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.329-342
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• 2019

In this paper, we introduce the notion of L-fuzzy semi-prime ideals and the radical of L-fuzzy ideals in universal algebras and make a theoretical study on their basic properties.

• East Asian mathematical journal
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• v.15 no.2
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• pp.177-190
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• 1999

In this work, we study permuting tri-derivations and give an example.