Publication details

On injective constructions of S-semigroups



Year of publication 2019
Type Article in Periodical
Magazine / Source Fuzzy Sets and Systems
MU Faculty or unit

Faculty of Science

Keywords Residuated poset; S-semigroup; Order-embedding; Subhomomorphism; Lattice-valued sup-lattice; Sup-algebra; Quantale; Q-module; S-semigroup quantale; Injective object; Injective hull; Semicategory; Quantaloid
Description In this paper, we continue the study of injectivity for fuzzy-like structures. We extend the results of Zhang and Laan for partially ordered semigroups to the setting of S-semigroups. We first characterize injectives in the category Ssgr (<=) of S-semigroups with subhomomorphisms as S-semigroup quantales. Second, we show that every S-semigroup has an epsilon(<=)-injective hull, and give its concrete form. Third, connections to ordered semicategories and quantaloids are indicated. In particular, if S is a commutative quantale, then the injectives in the category of S-semigroups with subhomomorphisms generalize the quantale algebras introduced by Solovyov. Quantale algebras provide a convenient universally algebraic framework for developing lattice-valued analogues of fuzzification. (C) 2019 Elsevier B.V. All rights reserved.
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