We systemize a number of algebras that are especially known in the
field of quantum structures and that in particular arise from the
positive cones of partially ordered groups. Generalized effect
algebras, generalized difference posets, cone algebras, commutative
BCK-algebras with the relative cancellation property, and positive
minimal clans are included in the text.

All these structures are conveniently characterizable as special
cases of generalized pseudo-effect algebras, which we introduced in
a previous paper. We establish the exact relations between all
mentioned structures, thereby adding new structures whenever
necessary to make the scheme of order complete.

Generalized pseudo-effect algebras were under certain conditions
proved to be representable by means of a \pogr{}. From this fact, we
will easily establish representation theorems for all of the
structures included in discussion.
