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Pseudoeffect algebras. II: Group representations. (English) Zbl 0994.81009
For the notation and terminology, see the review of Part I [ibid. 40, No. 3, 685–701 (2001; Zbl 0994.81008)].
The main result of the second part of the paper is the representation theorem which states that every pe.a. having RDP\(_1\) is an interval pe.a. Furthermore, the categories of pe.a.s and of unital po-groups, both having RDP\(_1\), are shown to be equivalent. It is also demonstrated that pseudo-MV algebras (introduced by G. Georgescu and A. Iorgulescu in a forthcoming paper) are pe.a.s with an additional structure.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06F15 Ordered groups
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