Quotients of dimension effect algebras

Abstract

We show that the quotient of a dimension effect algebra by its dimension equivalence relation is a unital bounded lattice-ordered positive partial abelian monoid that satisfies a version of the Riesz decomposition property. For a dimension effect algebra of finite type, the quotient is a centrally orthocomplete Stone–Heyting MV-effect algebra; moreover, an orthocomplete effect algebra in which equality is a dimension equivalence relation is the same thing as a complete Stone–Heyting MV-effect algebra.