Korean J. Math.  Vol 21, No 2 (2013)  pp.171-180
DOI: https://doi.org/10.11568/kjm.2013.21.2.171

Fuzzy semigroups in reductive semigroups

Inheung Chon

Abstract


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.


Subject classification

20N25

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ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr