Vol. 41, No. 3, 1972

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Partial algebraic structures associated with orthomodular posets

Stanley P. Gudder

Vol. 41 (1972), No. 3, 717–730

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.

Mathematical Subject Classification
Primary: 08A25
Received: 20 September 1970
Revised: 21 October 1971
Published: 1 June 1972
Stanley P. Gudder