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 |
Abstract: | 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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