|Authors:||Bleblou, Omalkhear Salem Almabruk
|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||Abstract:||
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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