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Soft ordered semigroups. (English) Zbl 1191.06009
If S and A are two nonempty sets, the pair (,A) is called a soft set over S if is a mapping of A into the set of all subsets of S [D. Molodtsov, Comput. Math. Appl. 37, No. 4–5, 19–31 (1999; Zbl 0936.03049)]. An ordered semigroup S is called a soft ordered semigroup if there is a nonempty set A and a soft set (,A) over S satisfying the following property: If xA such that (x), then (x) is a subsemigroup of S. An ordered semigroup S is called l-idealistic (resp. r-idealistic) soft ordered semigroup if there is a nonempty set A and a soft set (,A) over S such that (x) is a left (resp. right) ideal of S for every xA. For the definition of homomorphism between ordered semigroups given in the introduction of the paper we refer to [N. Kehayopulu and M. Tsingelis, Semigroup Forum 50, No. 2, 161–177 (1995; Zbl 0823.06010)].
06F05Ordered semigroups and monoids