Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields - Jorge Jimenez; María Luisa Serrano; Branimir Šešelja; Andreja Tepavčević (Axioms, 2023)
Omega rings (<semantics>Ω</semantics>-rings) (and other related structures) are lattice-valued structures (with <semantics>Ω</semantics> being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, <semantics>Ω</semantics>-ideals are introduced, and natural connections with <semantics>Ω</semantics>-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over <semantics>Ω</semantics>-fields is developed.