• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.9-14
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• 2007

In this paper, we introduce more extended special sets in implicative semigroups, and obtain some relations with ordered filters.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.95-100
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• 2006

In this paper we give some new characterizations of the intra-regular ordered semigroups in terms of bi-ideals and quasi-ideals, bi-ideals and left ideals, bi-ideals and right ideals of ordered semigroups.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.357-370
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• 2015

In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.627-637
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• 2013

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.1-6
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• 1998

The paper refers to ordered semigroups in which $x^2 (x \in S)$ are left ideal elements. We mainly show that this $po$-semigroup is left regular if and only if S is a union of left simple subsemigroups of S.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.235-243
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• 2009

In this paper, we introduce the notion of intuitionistic fuzzy semiprimality in an ordered semigroup, which is an extension of fuzzy semiprimality and investigate some properties of intuitionistic fuzzification of the concept of several ideals.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.131-135
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• 1997

We give the relation between the semilattice congruence N and the set of prime ideals of the ordered $\Gamma$-semigroup M.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.545-558
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• 2017

In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m,(p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m,(p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m,(p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1217-1225
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• 2010

In this paper we define fuzzy interior $\Gamma$-ideals in ordered $\Gamma$-semigroups. We prove that in regular(resp. intra-regular) ordered $\Gamma$-semigroups the concepts of fuzzy interior $\Gamma$-ideals and fuzzy $\Gamma$-ideals coincide. We prove that an ordered $\Gamma$-semigroup is fuzzy simple if and only if every fuzzy interior $\Gamma$-ideal is a constant function. We characterize intra-regular ordered $\Gamma$-semigroups in terms of interior (resp. fuzzy interior) $\Gamma$-ideals.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.149-154
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• 1998

We consider the ordered ${\Gamma}$-semigroups in which $x{\gamma}x(x{\in}M,{\gamma}{\in}{\Gamma})$ are left elements. We show that this $po-{\Gamma}$-semigroup is left regular if and only if M is a union of left simple sub-${\Gamma}$-semigroups of M.