• 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.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.425-436
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• 2022

In this paper we introduce the notion of 2-absorbing primary ideals of a commutative semigroup. We establish the relations between 2-absorbing primary ideals and prime, maximal, semiprimary and 2-absorbing ideals. We obtain various characterization theorems for commutative semigroups in which 2-absorbing primary ideals are prime, maximal, semiprimary and 2-absorbing ideals. We also study some other important properties of 2-absorbing primary ideals of a commutative semigroup.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.29-41
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• 2022

We study the concept of a quasi-ideal and a generalized bi-ideal of an n-ary semigroup; give a construction of the quasi-ideal of an n-ary semigroup generated by its nonempty subset; and introduce the notions of regularities, namely, a left regularity and a left weakly regularity. Moreover, the notions of a right regularity, a right weak regularity and a complete regularity are given. Finally, characterizations of these regularities are presented.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.251-267
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• 2020

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of non-Weierstrass points on a smooth plane curve of degree 5. First we find the candidates of semigroups by computing the dimensions of linear series on the curve. Then, by constructing examples of smooth plane curves of degree 5, we prove that each of the candidates is actually a Weierstrass semigroup at some pair of points on the curve. We need to study the systems of quadratic curves, which cut out the canonical series on the plane curve of degree 5.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.23-35
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• 2012

Given a set ${\Omega}$ and the notion of bipolar valued fuzzy sets, the concept of a bipolar ${\Omega}$-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar ${\Omega}$-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar ${\Omega}$-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar ${\Omega}$-fuzzy sub-semigroup is provided, and normal bipolar ${\Omega}$-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar ${\Omega}$-fuzzy sub-semigroups become bipolar ${\Omega}$-fuzzy sub-semigroups are considered.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.577-586
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• 2000

For a grading monoid S, we prove that (1) if (S, M) is a valuation semigroup, then M is an m-canonical ideal, that is, an ideal M such that M : (M:J)=J for every ideal J of S. (2) if S is an integrally closed semigroup and S has a principal m-canonical ideal, then S is a valuation semigroup, and (3) if S is a completely integrally closed and S has an m-canonical ideal I, then every ideal of S is I-invertible, that is, J+(I+J)=I for every ideal J of S.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.895-908
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• 2016

Firstly, we establish spectral mapping theorems for normal eigenvalues (due to Browder) of a $C_0$-semigroup and its generator. Secondly, we discuss relationships between normal eigenvalues of the compact monodromy operator and the generator of the evolution semigroup on $P_{\tau}(X)$ associated with the ${\tau}$-periodic evolutionary process on a Banach space X, where $P_{\tau}(X)$ stands for the space of all ${\tau}$-periodic continuous functions mapping ${\mathbb{R}}$ to X.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.323-330
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• 2007

In this paper we introduce the notion of strongly regular near-subtraction semigroups (right). We have shown that a near-subtraction semigroup X is strongly regular if and only if it is regular and without non zero nilpotent elements. We have also shown that in a strongly regular near-subtraction semigroup X, the following holds: (i) Xa is an ideal for every a $\in$ X (ii) If P is a prime ideal of X, then there exists no proper k-ideal M such that P $\subset$ M (iii) Every ideal I of X fulfills $I=I^2$.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.89-114
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• 2016

In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.