## States and idempotents of pseudo MV-algebras.(English)Zbl 0997.03050

Pseudo MV-algebras are non-commutative generalizations of MV-algebras. The study of states defined on a pseudo MV-algebra was started by the author in “States on pseudo MV-algebras” [Stud. Log. 68, 301-327 (2001; Zbl 0999.06011)].
This paper is concerned with the states on a pseudo MV-algebra $$A$$ satisfying general comparability, a condition on the Boolean algebra BCA of idempotents of $$A$$. A first result shows that every pseudo MV-algebra satisfying general comparability has at least one state. A second result asserts that in such a pseudo MV-algebra $$A$$, the space $${\operatorname {Ext}}\bigl (S(A)\bigr)$$ of extremal states on $$A$$ is homeomorphic to the space $${\operatorname {Ext}}\bigl (S(\operatorname {BCA})\bigr)$$ of extremal states on BCA.

### MSC:

 03G12 Quantum logic 06D35 MV-algebras 03B50 Many-valued logic

### Keywords:

pseudo MV-algebra state; general comparability; idempotent

Zbl 0999.06011