NEARLY COMMUTATIVE PSEUDOEFFECT ALGEBRAS

Thomas Vetterlein

   Pseudoeffect (PE-) algebras generalize effect algebras in no longer being necessarily commutative. We consider here those PE-algebras which are po-groups intervals and which are non-commutative only on the infinitesimal level. In particular, intervals of the lexicographical product of an abelian and a possibly nonabelian po-group are included in the discussion. We show that PE-algebras of the considered type possess a non-trivial commutative homomorphic image. A consequence of this fact is that they possess a non-empty state space.

Keywords: pseudoeffect algebras, po-groups, PE-algebras with Riesz properties

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