LATTICE EFFECT ALGEBRAS DENSELY EMBEDDABLE INTO COMPLETE ONES

An effect algebraic partial binary operation circle plus defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion (E) over cap of E there exists an effect algebraic partial binary operation (circle plus) over cap then (circle plus) over cap need not be an extension of circle plus. Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for that (circle plus) over cap existing on (E) over cap is an extension of circle plus defined on E. Further we show that such (circle plus) over cap extending circle plus exists at most one.