• 한국지능시스템학회논문지
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• 제15권6호
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• pp.771-779
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• 2005

We introduce two concepts of intuitionistic fuzzy Rees congruence on a semigroup and intuitionistic fuzzy Rees con-gruence semigroup. As an important result, we prove that for a intuitionistic fuzzy Rees congruence semigroup S, the set of all intuitionistic fuzzy ideals of S and the set of all intuitionistic fuzzy congruences on S are lattice isomorphic. Moreover, we show that a homomorphic image of an intuitionistic fuzzy Rees congruence semigroup is an intuitionistic fuzzy Rees congruence semigroup.

• 대한수학회논문집
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• 제26권3호
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• pp.373-384
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• 2011

In this paper we introduce and give some characterizations of (m, n)-regular le-${\Gamma}$-semigroup in terms of (m, n)-ideal elements and (m, n)-quasi-ideal elements. Also, we give some characterizations of subidempotent (m, n)-ideal elements in terms of $r_{\alpha}$- and $l_{\alpha}$- closed elements.

• 대한수학회논문집
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• 제13권3호
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• pp.501-513
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• 1998

In this paper, we deal with the asymptotic behavior for the almost-orbits {u(t)} of an asymptotically nonexpansive semigroup S = {S(t) : t $\in$ G} for a right reversible semitopological semigroup G, defined on a suitable subset C of Banach spaces with the Opial's condition, locally uniform Opial condition, or uniform Opial condition.

• 대한수학회논문집
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• 제12권2호
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• pp.237-250
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• 1997

In this paper, we study the asymptotic behavior of orbits ${S(t)x}$ of an asymptotically nonexpansive semigroup $S = {S(t) : t \in G}$ for a right reversible semitopological semigroup G, defined on a weakly compact convex subset C of Banach spaces with Opial's condition for any $x \in C$.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.375-381
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• 2012

We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in an ordered ternary semigroup and study their properties. Also regular ordered ternary semigroup is defined and several ideal-theoretical characterizations of the regular ordered ternary semigroups are furnished.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.527-537
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• 2005

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy bi-ideals of an ordered semigroup are investigated.

• 대한수학회지
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• 제58권6호
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• pp.1367-1383
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• 2021

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into a numerical semigroup and its dual. It is also given exactly for what kind of numerical semigroup S, the semigroup ring 𝕜⟦S⟧ has at least one Gorenstein subring and has at least one Kunz subring.

• 충청수학회지
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• 제33권3호
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• pp.339-349
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• 2020

Let P ⋊ ℕ^x be a semidirect product of an additive semigroup P = {0, 2, 3, ⋯ } by a multiplicative positive natural numbers semigroup ℕ^x. We consider a covariant semigroup C^∗-algebra 𝓣(P ⋊ ℕ^x) of the semigroup P ⋊ ℕ^x. We obtain the condition that a state on 𝓣(P ⋊ ℕ^x) can be a ground state of the natural C^∗-dynamical system (𝓣(P ⋊ ℕ^x), ℝ, σ).

• 대한수학회보
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• 제43권2호
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• pp.333-341
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• 2006

We analyze a detailed picture of the algebraic structure of $C^*$-algebras generated by isometric representations of the non-amenable semigroup P = {0,2,3,...,N,...}.

• 호남수학학술지
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• 제41권3호
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• pp.505-514
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• 2019

In this paper, some results are obtained from studying convolution on the spectrum of full transformation semigroup and some of its subsemigroups using Cayley's table. The shift of ${\alpha}$ determines its eigenvalues and one-dimensional linear convolution is complex in Symmetric group.