• 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.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.55-82
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• 2019

Given ${\sigma}:G{\rightarrow}G$ an involutive automorphism of a semigroup G, we study the solutions and stability of the following functional equations $$f(x{\sigma}(y))=f(x)g(y)+g(x)f(y),\;x,y{\in}G,\\f(x{\sigma}(y))=f(x)f(y)-g(x)g(y),\;x,y{\in}G$$ and $$f(x{\sigma}(y))=f(x)g(y)-g(x)f(y),\;x,y{\in}G$$, from the theory of trigonometric functional equations. (1) We determine the solutions when G is a semigroup generated by its squares. (2) We obtain the stability results for these equations, when G is an amenable group.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.357-368
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• 2019

We define the concepts of the first and the second module dual of a Banach space X. And also bring a new concept of module amenability for a Banach algebra ${\mathcal{A}}$. For inverse semigroup S, we will give a new action for ${\ell}^1(S)$ as a Banach ${\ell}^1(E_S)$-module and show that if S is amenable then ${\ell}^1(S)$ is ${\ell}^1(E_S)$-module amenable.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.343-351
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• 2013

In this paper, the dynamics on a transcendental entire semigroup G is investigated. We show the possible values of any limit function of G in strictly wandering domains and Fatou components, respectively. Moreover, if G is of class $\mathfrak{B}$, for any $z$ in a Fatou domain, there does not exist a sequence $\{g_k\}$ of G such that $g_k(z){\rightarrow}{\infty}$ as $k{\rightarrow}{\infty}$.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.25-36
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• 2009

We compute spectrums of left regular isometries and weighted left regular isometries of a strongly perforated semigroup $P=\{0,2,3,4,{\cdots}\}$.

• 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.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.461-468
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• 2008

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.259-266
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• 2011

We apply the concept of interval-valued fuzzy sets to theory of semigroups. We give some properties of interval-valued fuzzy ideals and interval-valued fuzzy bi-ideals, and characterize which is left [right] simple, left [right] duo and a semilattice of left [right] simple semigroups or another type of semigroups in terms of interval-valued fuzzy ideals and intervalvalued fuzzy bi-ideals.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1125-1135
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• 2018

We show that for an M-action on a compact Hausdorff uniform space, if it has at least two disjoint compact invariant subsets, then it is thickly syndetically sensitive. Additionally, we point out that for a P-M-action of a discrete abelian group on a compact Hausdorff uniform space, the multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.753-759
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• 1995

Let C be a smooth complex algebraic curve of genus g. For a divisor D on C, dim D means the dimension of the complete linear series $\mid$D$\mid$ containing D, which is the same as the projective dimension of the vector space of meromorphic functions f on C with divisor of poles $(f)_\infty \leq D$.