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@article{1775038,
author = {Zhang, Xia and Paseka, Jan},
article_location = {New York},
article_number = {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},
language = {eng},
issn = {0020-7748},
journal = {International Journal of Theoretical Physics},
title = {The MacNeille Completions for Residuated S-Posets},
url = {https://doi.org/10.1007/s10773-019-04046-2},
volume = {60},
year = {2021}
}
TY - JOUR
ID - 1775038
AU - Zhang, Xia - Paseka, Jan
PY - 2021
TI - The MacNeille Completions for Residuated S-Posets
JF - International Journal of Theoretical Physics
VL - 60
IS - 2
SP - 667-676
EP - 667-676
PB - Springer
SN - 00207748
KW - Residuated poset
KW - S-semigroup
KW - Residuated S-poset
KW - Order-embedding
KW - Subhomomorphism
KW - Lattice-valued sup-lattice
KW - Sup-algebra
KW - Quantale
KW - Q-module
KW - Q-algebra
KW - S-semigroup quantale
KW - Injective object
KW - Injective hull
UR - https://doi.org/10.1007/s10773-019-04046-2
N2 - 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.
ER -
ZHANG, Xia a Jan PASEKA. The MacNeille Completions for Residuated S-Posets. \textit{International Journal of Theoretical Physics}. New York: Springer, 2021, roč.~60, č.~2, s.~667-676. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-019-04046-2.
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