Partial algebraic structures associated with orthomodular posets
Stanley Gudder · Pacific Journal of Mathematics · 1972
In this paper there are three main results: I.An orthomodular poset with property C is essentially the same as an associative partial Boolean algebra.II.If P is an orthomodular poset, then S(P), the set of residuated maps on P, can be made into a weak partial Baer*semigroup is such a way that P is isomorphic to the orthomodular poset of closed projections in S(P).III.If (P, M) is a conditional quantum logic, then the collection of all finite compositions of primitive operations (satisfying certain technical conditions) is a partial Baer*-semigroup.It is assumed that the reader is familiar with the rudiments of the theory of orthomodular posets.