
{\bf Existence of states on pseudoeffect algebras}

{\it Thomas Vetterlein}


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ABSTRACT:

Pseudoeffect (PE-) algebras have been introduced as a
non-commutative generalization of effect algebras. We study
in this paper PE-algebras with the special property of
having a non-empty state space.

To this end, we consider PE-algebras which are, in a certain
sense, non-commutative only in the small. Such an PE-algebra
is shown to possess a non-trivial commutative homomorphic
image -- which is equivalent to saying that there exist
states. A typical example is given by an interval of the
lexicographical product of two \pogr{}s the first of which
is abelian.



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{\it AMS classification (1991): }
03G12, 81P10, 06F05, 06F15

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{\it Keywords: }
pseudoeffect algebras, $po$-groups, PE-algebras with Riesz properties

