Subcentral Ideals in Generalized Effect Algebras

Abstract

In this paper, we introduce subcentral ideals in the class of cancellative positivepartial abelian monoids (CPAMs). Every complementary pair of subcentral idealsin a CPAM P corresponds to a subdirect decomposition of P. If this decompositionis direct, the corresponding ideals are called central. Subcentral ideals arecharacterized as central elements in the lattice of the recently introducedso-called R1-ideals. Every subcentral ideal is a central element in the lattice of allideals. A subcentral ideal I is central iff I is Riesz ideal. In an upper-directedCPAM, every subcentral ideal is central.