Chains of archimedean ordered semigroups by terms of fuzzy subsets
نویسنده
چکیده
In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an ordered semigroup S to be a chain of archimedean (r-archimedean, t-archimedean) ordered subsemigroups are also given by means of fuzzy subsets of S. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup S is a chain of archimedean ordered subsemigroups if and only if S is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of S form a chain. Keywords—Ordered fuzzy point, archimedean (r-archimedean, tarchimedean) ordered semigroup, completely semiprime fuzzy ideal, weakly completely prime fuzzy ideal.
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