TENSOR PRODUCT OF DIFFERENCE POSETS AND EFFECT ALGEBRAS

A tenser product of difference posets and/or, equivalently, of effect algebras, which generalize orthoalgebras and orthomodular posers, is defined, and an equivalent condition is presented. The proof uses the notion of D-test spaces generalizing test spaces of Randall and Foulis. in particular, we show that a tenser product for difference posers with a nonempty system of probability measures exists.