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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 and Jan PASEKA. On injective constructions of S-semigroups. \textit{Fuzzy Sets and Systems}. Amsterdam: Elsevier, 2019, vol.~373, OCT 15 2019, p.~78-93. ISSN~0165-0114. Available from: https://dx.doi.org/10.1016/j.fss.2019.02.012.
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