Good and bad infinitesimals, and states on pseudo MV-algebras (Q2573721)

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.