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Zbl 1191.06009
Jun, Young Bae; Lee, Kyoung Ja; Khan, Asghar
Soft ordered semigroups. (English)
[J] Math. Log. Q. 56, No. 1, 42-50 (2010). ISSN 0942-5616; ISSN 1521-3870/e

If $S$ and $A$ are two nonempty sets, the pair $({\cal F},A)$ is called a {\it soft set} over $S$ if $\cal F$ is a mapping of $A$ into the set of all subsets of $S$ [{\it D. Molodtsov}, Comput. Math. Appl. 37, No.~4--5, 19--31 (1999; Zbl 0936.03049)]. An ordered semigroup $S$ is called a {\it soft ordered semigroup} if there is a nonempty set $A$ and a soft set $(\cal F, A)$ over $S$ satisfying the following property: If $x\in A$ such that ${\cal F} (x)\not=\emptyset$, then ${\cal F} (x)$ is a subsemigroup of $S$. An ordered semigroup $S$ is called {\it $l$-idealistic} (resp. {\it $r$-idealistic}) {\it soft ordered semigroup} if there is a nonempty set $A$ and a soft set $({\cal F}, A)$ over $S$ such that ${\cal F}(x)$ is a left (resp. right) ideal of $S$ for every $x\in A$. For the definition of homomorphism between ordered semigroups given in the introduction of the paper we refer to [{\it N. Kehayopulu} and {\it M. Tsingelis}, Semigroup Forum 50, No. 2, 161--177 (1995; Zbl 0823.06010)].
[Niovi Kehayopulu (Athens)]

MSC 2000:: *06F05 Ordered semigroups

Keywords: ordered semigroup; soft set; soft ordered semigroup; idealistic soft ordered semigroup

Citations: Zbl 0936.03049; Zbl 0823.06010

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