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@article{1601558, author = {Zhang, Xia and Paseka, Jan}, article_location = {Amsterdam}, article_number = {OCT 15 2019}, 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}, language = {eng}, issn = {0165-0114}, journal = {Fuzzy Sets and Systems}, title = {On injective constructions of S-semigroups}, url = {https://www.sciencedirect.com/science/article/pii/S0165011419301435?via%3Dihub}, volume = {373}, year = {2019} }
TY - JOUR ID - 1601558 AU - Zhang, Xia - Paseka, Jan PY - 2019 TI - On injective constructions of S-semigroups JF - Fuzzy Sets and Systems VL - 373 IS - OCT 15 2019 SP - 78-93 EP - 78-93 PB - Elsevier SN - 01650114 KW - Residuated poset KW - S-semigroup KW - Order-embedding KW - Subhomomorphism KW - Lattice-valued sup-lattice KW - Sup-algebra KW - Quantale KW - Q-module KW - S-semigroup quantale KW - Injective object KW - Injective hull KW - Semicategory KW - Quantaloid UR - https://www.sciencedirect.com/science/article/pii/S0165011419301435?via%3Dihub L2 - https://www.sciencedirect.com/science/article/pii/S0165011419301435?via%3Dihub N2 - 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. ER -
ZHANG, Xia a Jan PASEKA. On injective constructions of S-semigroups. \textit{Fuzzy Sets and Systems}. Amsterdam: Elsevier, 2019, roč.~373, OCT 15 2019, s.~78-93. ISSN~0165-0114. Dostupné z: https://dx.doi.org/10.1016/j.fss.2019.02.012.
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