Omega Ideals in Omega Rings and Systems of Linear Equations over Omega Fields

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.