The Center Of A Generalized Effect Algebra

Abstract

In this article, we study the center of a generalized effect algebra (GEA), relate it to the exocenter, and in case the GEA is centrally orthocomplete (a COGEA), relate it to the exocentral cover system. Our main results are that the center of a COGEA is a complete boolean algebra and that a COGEA decomposes uniquely as the direct sum of an effect algebra (EA) that contains the center of the COGEA and a complementary direct summand in which no nonzero direct summand is an EA.

Keywords

• effect algebra
• generalized effect algebra
• boolean effect algebra
• direct sum decomposition
• center
• exocenter
• orthosummable family
• exocentral cover
• centrally orthocomplete