On injective constructions of S-semigroups

J 2019

On injective constructions of S-semigroups

ZHANG, Xia and Jan PASEKA

Basic information

Original name

On injective constructions of S-semigroups

Authors

ZHANG, Xia and Jan PASEKA

Edition

Fuzzy Sets and Systems, Amsterdam, Elsevier, 2019, 0165-0114

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 3.305

RIV identification code

RIV/00216224:14310/19:00107981

Organization unit

Faculty of Science

DOI

https://doi.org/10.1016/j.fss.2019.02.012

UT WoS

000482585800005

EID Scopus

2-s2.0-85061967343

Keywords in English

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

Abstract

In the original language

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.

Links

GF15-34697L, research and development project

Name: Nové přístupy k reziduovaným posetům

Investor: Czech Science Foundation, Partner Agency (Austria)

Cite

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

@article{1601558,
   author = {Zhang, Xia and Paseka, Jan},
   article_location = {Amsterdam},
   article_number = {OCT 15 2019},
   doi = {https://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://doi.org/10.1016/j.fss.2019.02.012.

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