Higher degrees of distributivity in complete generalized MV-algebras

Abstract

Abstract We apply the notion of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis. Let M be a complete GMV-algebra and let α be a cardinal. We prove that M is α-distributive if and only if it is (α, 2)-distributive. We deal with direct summands of M which are homogeneous with respect to higher degrees of distributivity.