• Title/Summary/Keyword: Semigroup

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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.

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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.

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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).

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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([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.

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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 ([1],[3],[4] and [5]).

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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.

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QUANTUM DYNAMICAL SEMIGROUP AND ITS ASYMPTOTIC BEHAVIORS

  • Choi, Veni
    • 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.

INT-SOFT SEMIGROUPS WITH TWO THRESHOLDS

  • Kong, In Suk
    • Honam Mathematical Journal
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    • v.38 no.1
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    • pp.95-125
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    • 2016
  • In this paper, we study more general version of the paper [J. H. Lee, I. S. Kong, H. S. Kim and J. U. Jung, Generalized int-soft subsemigroups, Ann. Fuzzy Math. Inform. 8(6) (2014) 869-887]. We introduce the notion of int-soft semigroup with two thresholds ${\varepsilon}$ and ${\delta}$ (briefly, (${\varepsilon}$, ${\delta}$)-int-soft semigroup) of a semigroup S, and investigate several related properties.

CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS

  • Iampan, Aiyared
    • Journal of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.775-784
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    • 2009
  • In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].