Two-valued states on Baer \(^\ast\)-semigroups (Q2447096)

In a recent paper by the authors [Rep. Math. Phys. 68, No. 1, 65--83 (2011; Zbl 1301.81018)] a general framework was given for the study of families of two-valued states on orthomodular lattices. These ideas are now applied in research of states on Baer \(^\ast\)-semigroups. A special attention is paid to the class of all two-valued states and to its subclass of Jauch-Piron two-valued states. Also, an algebraic approach to two-valued states on Baer \(^\ast\)-semigroups is developed: the latter are enriched with a unary operation that allows to introduce an equational theory of two-valued states on Baer \(^\ast\)-semigroups.