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 | 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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