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Good and bad infinitesimals, and states on pseudo MV-algebras. (English) Zbl 1081.06010
Pseudo MV-algebras are a noncommutative generalization of MV-algebras. States on pseudo MV-algebras are analogues of probability measures. In contrast to MV-algebras, there are pseudo MV-algebras having no states. By a crucial result of the second author, pseudo MV-algebras can be represented as intervals of unital \(\ell \)-groups. The authors use this representation to study the problem of existence of states on pseudo MV-algebras by means of the properties of their sets of infinitesimal elements and two kinds of their radicals. Moreover, they give many interesting and important examples of pseudo MV-algebras which describe different classes and varieties of pseudo MV-algebras.

MSC:
06D35 MV-algebras
03G12 Quantum logic
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