Two-Valued States on Baer *-Semigroups

Abstract

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer *semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer * -semigroups. Proposition 2.1 Let L be an orthomodular lattice. Then we have: 1. Z(L) is a Boolean sublattice of L [20, Theorem 4.15].2. z ∈ Z(L) iff for each a ∈ L, a = (a ∧ z) ∨ (a ∧ ¬z) [20, Lemma 29.9].