The number of distinct operations (that is, the range of the variable a) may be infinite, but for our main result (Theorem 2), we shall require every n(a) to be finite—that is, it will concern algebras with finitary operations. The concepts of subalgebra, congruence relation on an algebra, homomorphism of one algebra A onto (or into) another algebra with the same operations, and of the direct u...

We prove that every MV-effect algebra M is, as an effect algebra, a homomorphic image of its R-generated Boolean algebra. We characterize central elements of M in terms of the constructed homomorphism. 1. Definitions and basic relationships An effect algebra is a partial algebra (E;⊕, 0, 1) with a binary partial operation ⊕ and two nullary operations 0, 1 satisfying the following conditions. (E...