| Affiliation: | (1) Dep. Math. Inform., University of Salerno, Via Ponte don Melillo, I-84084 Fisciano, Salerno, Italy;(2) Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia;(3) Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01 Košice, Slovakia |
| Abstract: | We study relations among the set of infinitesimal elements of pseudo MV-algebras and the problem of existence of states on them. This is important because in contrast to MV-algebras, it can happen that a pseudo MV-algebra has no states, so no probabilistic evaluation of events on it is possible. We introduce two kinds of radicals, and we deal with their relation. In some cases, they are completely different, which is not the case for MV-algebras. We give many interesting examples describing different situations, and we deal in more details with a subvariety of symmetric pseudo MV-algebras, where both complements coincide. Mathematics Subject Classifications (2000) 06D35, 03B50, 03G12. |
