The MacNeille Completions for Residuated S-Posets
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1007/s10773-019-04046-2 |
| Doi | http://dx.doi.org/10.1007/s10773-019-04046-2 |
| Keywords | Residuated poset; S-semigroup; Residuated S-poset; Order-embedding; Subhomomorphism; Lattice-valued sup-lattice; Sup-algebra; Quantale; Q-module; Q-algebra; S-semigroup quantale; Injective object; Injective hull |
| Description | In this paper, we continue the study of injectivity for fuzzy-like structures. We extend the results of Zhang and Paseka for S-semigroups to the setting of residuated S-posets. It turns out that every residuated S-poset over a quantale S embeds into its MacNeille completion as its E?-injective hull. In particular, if S is a commutative quantale, then the injectives in the category of residuated S-posets with subhomomorphisms are precisely the quantale algebras introduced by Solovyov. Quantale algebras provide a convenient universally algebraic framework for developing lattice-valued analogues of fuzzification. |
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