On injective constructions of S-semigroups

Warning

This publication doesn't include Faculty of Arts. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

ZHANG Xia PASEKA Jan

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

Faculty of Science

Citation
Web https://www.sciencedirect.com/science/article/pii/S0165011419301435?via%3Dihub
Doi http://dx.doi.org/10.1016/j.fss.2019.02.012
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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.