• Korean Journal of Mathematics
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• v.14 no.2
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• pp.273-280
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• 2006

Lipschitzian semigroup is a semigroup of Lipschitz operators which contains $C_0$ semigroup and nonlinear semigroup. In this paper, we establish the cannonical exponential formula of Lipschitzian semigroup from its Lie generator and the approximation theorem by Laplace transform approach to Lipschitzian semigroup.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.363-371
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• 2018

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.171-180
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• 2013

We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.87-91
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• 2002

This note consists of some efficient examples to support the notion of enveloping semigroup compactification and also employ this notion to obtain the universal reductive compactification.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.503-512
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• 2003

In this paper, we first give an alternative description of the fundamental orthodox semigroup $\bar{A}$(1, 2). We then use this to represent the double four-spiral semigroup $DSp_4$ as a regular Rees matrix semigroup over $\bar{A}$(1, 2).

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.707-722
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• 2023

The purpose of this paper is to obtain the commutativity of a gamma dominion for a commutative gamma semigroup by using Isbell zigzag theorem for gamma semigroup and we prove some gamma semigroup identities are preserved under epimorphism. Moreover, we extend epimorphism, dominion and Isbell zigzag theorem for partially ordered semigroup to partially ordered gamma semigroup.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.406-410
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• 2003

B. M. Schein([1]) considered systems of the form (${\Phi}$; ${\circ}$,-), where ${\Phi}$ is a set of functions closed under the composition "${\circ}$" of functions and the set theoretic subtraction "-". In this structure, (${\Phi}$; ${\circ}$) is a function semigroup and (${\Phi}$;-) is a subtraction algebra in the sense of [1]. He proved that every subtraction semigroup is isomorphic to a difference semigroup of invertible functions. Also this structure is closely related to the mathematical logic, Boolean algebra, Bck-algera, etc. In this paper, we define the near subtraction semigroup as a generalization of the subtraction semigroup, and define the notions of strong for it, and then we will search the general properties of this structure, the properties of ideals, and the application of it.

• East Asian mathematical journal
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• v.22 no.2
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• pp.189-194
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• 2006

Throughout this paper, a semigroup S will denote a torsion free grading monoid, and it is a non-zero semigroup with 0. The operation is written additively. The aim of this paper is to study semigroup version of an integral domain ([1],[3],[4] and [5]).

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.203-209
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• 1988

In this paper, we define a g-regular semigroup which is a generalization of a regular semigroup. And we want to find some properties of g-regular semigroup. G-regular semigroups contains the variety of all regular semigroup and the variety of all periodic semigroup. If a is an element of a semigroup S, the smallest left ideal containing a is Sa.cup.{a}, which we may conveniently write as $S^{I}$a, and which we shall call the principal left ideal generated by a. An equivalence relation l on S is then defined by the rule alb if and only if a and b generate the same principal left ideal, i.e. if and only if $S^{I}$a= $S^{I}$b. Similarly, we can define the relation R. The equivalence relation D is R.L and the principal two sided ideal generated by an element a of S is $S^{1}$a $S^{1}$. We write aqb if $S^{1}$a $S^{1}$= $S^{1}$b $S^{1}$, i.e. if there exist x,y,u,v in $S^{1}$ for which xay=b, ubv=a. It is immediate that D.contnd.q. A semigroup S is called periodic if all its elements are of finite order. A finite semigroup is necessarily periodic semigroup. It is well known that in a periodic semigroup, D=q. An element a of a semigroup S is called regular if there exists x in S such that axa=a. The semigroup S is called regular if all its elements are regular. The following is the property of D-classes of regular semigroup.group.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.189-198
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• 2004

In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.