Omega rings (Ω-rings) (and other related structures) are lattice-valued structures (with Ω being the codomain lattice) defined on crisp algebras of the same type, with lattice-valued equality replacing the classical one. In this paper, Ω-ideals are introduced, and natural connections with Ω-congruences and homomorphisms are established. As an application, a framework of approximate solutions of systems of linear equations over Ω-fields is developed.
