• Title, Summary, Keyword: semigroup

### SEMIGROUP OF LIPSCHITZ OPERATORS

• Lee, Young S.
• 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.

### Fuzzy ideal graphs of a semigroup

• Rao, Marapureddy Murali Krishna
• 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.

### G-REGULAR SEMIGROUPS

• Sohn, Mun-Gu;Kim, Ju-Pil
• 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.

### FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS

• Chon, Inheung
• 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.

### THE REPEATED ENVELOPING SEMIGROUP COMPACTIFICATIONS

• FATTAHI, A.;MILNES, P.
• 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.

### Structure of the Double Four-spiral Semigroup

• CHANDRASEKARAN, V.M.;LOGANATHAN, M.
• 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).

### GENERALIZED IDEAL ELEMENTS IN le-Γ-SEMIGROUPS

• Hila, Kostaq;Pisha, Edmond
• Communications of the Korean Mathematical Society
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• v.26 no.3
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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.

### On Near Subtraction Semigroups (Near Subtraction Semigroups에 관한 연구)

• Yon Yong-Ho;Kim Mi-Suk;Kim Mi-Hye
• Proceedings of the Korea Contents Association Conference
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• pp.406-410
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• 2003
• B. M. Schein() 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 . 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.

### NOTES ON GRADING MONOIDS

• Lee, Je-Yoon;Park, Chul-Hwan
• 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 (,, and ).

### CONGRUENCE-FREE SIMPLE SEMIGROUP

• Moon, Eunho L.
• Korean Journal of Mathematics
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• v.13 no.2
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• pp.177-182
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• 2005
• If a semigroup S has no nontrivial congruences then S is either simple or 0-simple.() By contrast with ring theory, not every congruence on a semigroup is associated with an ideal, hence some simple(or 0-simple) semigroup may have a nontrivial congruence. Thus it is a short note for the characterization of a simple(or 0-simple) semigroup that is congruence-free. A semigroup that has no nontrivial congruences is said to be congruence-free.