Abstract
All known a quantum logicsoÐ orthomodular lattices and posets, orthoalgebras, effect algebras, etc.Ðmay be regarded as cancelative, unital partial abelian semigroups. [See Wilce (1995a, b) for pertinent definitions.] An abelian group may also be regarded as a cancelative, unital PASÐ one in which every element is a unit. As noted in Wilce (1995b), every cancelative unital PAS L has a canonical ideal A (L) which is an abelian group, and a canonical quotient by A (L) which is an effect algebra. Thus, we may regard every cancellative, unital PAS as an extension of an effect algebra by an abelian group. The present paper begins a study of such extensions.
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