• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.161-166
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• 2005

Let BQ be the class of all semigroups whose bi-ideals are quasi-ideals. It is known that regular semigroups, right [left] 0-simple semigroups and right [left] 0-simple semigroups belong to BQ. Every zero semigroup is clearly a member of this class. In this paper, we characterize when generalized full transformation semigroups and generalized Baer-Levi semigroups are in BQ in terms of the cardinalities of sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.2
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• pp.103-106
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• 2000

We introduce the concepts of TL-finite state machines TL-transformation semigroups and coverings and several decompositions of transformation semigroups and investigate some their algebraic structures.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.511-518
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• 2005

Necessary and sufficient conditions have been provided for some standard regressive transformation semigroups on a poset to be eventually regular. Our main purpose is to generalize this result by characterizing when their generalized semigroups are eventually regular.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.66-70
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• 1996

We investigate some of algebraic properties of T-generalized state machines, T-generalized transformation semigroups, coverings of T-generalized state machines and T-generalized transformation semigroups.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.467-486
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• 1999

We introduce the concepts of a generalized state machine and a generalized transformation semigroup and discuss their algebraic properties.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.227-238
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• 1999

We introduce several decompositons of generalized trans-formation semigroups and investigate some of their algebraic struc-tures.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.705-710
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• 2018

Let T(X) be the full transformation semigroup on a set X and ${\sigma}$ be an equivalence relation on X. Denote $$E(X,{\sigma})=\{{\alpha}{\in}T(X):{\forall}x,\;y{\in}X,\;(x,y){\in}{\sigma}\;\text{implies}\;x{\alpha}=y{\alpha}\}.$$. Then $E(X,{\sigma})$ is a subsemigroup of T(X). In this paper, we characterize two semigroups of type $E(X,{\sigma})$ when they are isomorphic.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1055-1062
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• 2014

Let $O_n$ and $PO_n$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_n=\{1,{\ldots},n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_n$ on the set $X_n$, under its natural order, is defined by $SPO_n=PO_n{\setminus}O_n$. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for $2{\leq}r{\leq}n-1$.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.273-283
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• 2001

We introduce sums and joins of T-fuzzy transformation semi-groups and investigate their algebraic structures.