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 Ideals in Omega Rings and Systems of Linear Equations over Omega Fields
Journal: Axioms
Volume: 12
Issue: 8
First page: 757
Issue Date: 2023
Rank: ~M21
ISSN: 2075-1680
DOI: 10.3390/axioms12080757
Omega rings ((Formula presented.) -rings) (and other related structures) are lattice-valued structures (with (Formula presented.) being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, (Formula presented.) -ideals are introduced, and natural connections with (Formula presented.) -congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over (Formula presented.) -fields is developed.
Keywords: complete lattice | fuzzy algebra | fuzzy congruence | fuzzy equality | ideals in rings | omega fields | omega ring | systems of linear equations
Publisher: MDPI

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