Quotients of dimension effect algebras (Q664310)

\textit{A. N.~Sherstnev} [Kazan. Gos. Univ., Uch. Zap. 128, No. 2, 48--62 (1968; Zbl 0235.02021)] and \textit{V. V.~Kalinin} [Algebra Logika 15, 535--557 (1976; Zbl 0377.06003)] studied the dimension equivalence relation on orthomodular posets. The current paper extends their results to more general structures, namely effect algebras. It is shown 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.