• Korean Journal of Mathematics
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• v.19 no.3
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• pp.321-330
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• 2011

We characterize the fuzzy bi-ideal generated by a fuzzy subset in a semigroup and the fuzzy bi-ideal generated by a fuzzy subset A such that $A{\subseteq}A^2$ in a semigroup with an identity element. Our work generalizes the characterization of fuzzy bi-ideals by Mo and Wang ([8]).

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.191-201
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• 2007

In this paper we introduce the notion of congruence on a ternary semigroup and study some interesting properties. We also introduce the notions of cancellative congruence, group congruence and Rees congruence and characterize these congruences in ternary semigroups.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.627-635
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• 2018

In this paper, we use the notion of characters of transformations provided in [8] by Purisang and Rakbud to define a notion of weak regularity of transformations on an arbitrarily fixed set X. The regularity of a semigroup of weakly regular transformations on a set X is also investigated.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.629-638
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• 2014

The concept of prime and weakly prime ideal in semigroups has been introduced by G. Szasz [4]. In this paper, we define the involution in po-${\Gamma}$-semigroups, then we extend some results on prime, semiprime and weakly prime ideals to the involution po-${\Gamma}$-semigroup S. Also, we characterize intra-regular involution po-${\Gamma}$-semigroups. We establish that in the involution po-${\Gamma}$-semigroup S such that the involution preserves the order, an ideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime ideals of S coincide. Finally, we prove that if S is a po-${\Gamma}$-semigroup with order preserving involution, then the ideals of S are prime if and only if S is intra-regular.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.603-607
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• 1995

This paper gives some basic properties on a disjoint decomposition of regular *-semigroups and shows thata regular *-semigroup with a left magnifying element has an identity element.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.261-266
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• 2003

In this paper, we described the structure of coextensions of regular semigroups by rectangular bands.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.483-507
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• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• East Asian mathematical journal
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• v.14 no.2
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• pp.393-397
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• 1998

The author obtains ideal-theoretical characterizations of the following two classes of $\Gamma$-semigroups; (1) regular $\Gamma$-semigroups; (2) $\Gamma$-semigroups that are both regular and intra-regular.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.215-225
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• 2012

We initiate the study of interval-valued fuzzy quasi-ideal of a semigroup. In Section 2, we list some basic definitions in the later sections. In Section 3, we investigate interval-valued fuzzy subsemigroups and in Section 4, we define interval-valued fuzzy quasi-ideals and establish some of their basic properties. In Section 5, we obtain characterizations of regular and intraregular semigroups using the machinery developed in the preceding sections.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.359-367
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• 2007

We consider the intuitionistic fuzzification of the concept of several ${\Gamma}$-ideals in a ${\Gamma}$-semigroup S, and investigate some properties of such ${\Gamma}$-ideals.