Authors: Jimenez, Jorge
Serrano, María Luisa
Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Omega-rings
Journal: Fuzzy Sets and Systems
Issue Date: 2022
Rank: ~M21a
ISSN: 0165-0114
DOI: 10.1016/j.fss.2022.04.012
Omega rings (Ω-rings) and some special types of these structures (commutative, without zero divisors, Ω-fields,...) are introduced and investigated. Ω is a complete lattice and Ω-rings are lattice-valued algebraic structures, defined on crisp algebras of the same type as rings, but which are not necessarily rings. The classical equality is replaced by a lattice-valued one. We give some basic properties of Ω-rings and related structures.
Keywords: A complete lattice | Fuzzy algebra | Fuzzy congruence | Fuzzy equality | Fuzzy identity | Omega ring
Publisher: Elsevier

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