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

Abstract

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