Authors: Bleblou, Omalkhear Salem Almabruk
Šešelja, Branimir
Tepavčević, Andreja 
Title: Normal Ω-subgroups
Journal: Filomat
Volume: 32
Issue: 19
First page: 6699
Last page: 6711
Issue Date: 1-Jan-2018
Rank: M22
ISSN: 0354-5180
DOI: 10.2298/FIL1819699B
Subgroups, congruences and normal subgroups are investigated for Ω-groups. These are lattice-valued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal Ω-subgroup is defined as a particular class in an Ω-congruence. Our main result is that the quotient groups over cuts of a normal Ω-subgroup of an Ω-group G, are classical normal subgroups of the corresponding quotient groups over G. We also describe the minimal normal Ω-subgroup of an Ω-group, and some other constructions related to Ω-valued congruences.
Keywords: Complete lattice | Fuzzy algebra | Fuzzy congruence | Fuzzy equality | Fuzzy group | Fuzzy identity
Publisher: Faculty of Sciences and Mathematics, University of Niš
Project: Development of methods of computation and information processing: theory and applications 

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