On a new construction of pseudo effect algebras
We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which are connected not necessarily with partially ordered groups, but rather with generalized pseudo effect algebras where the greatest element is not guaranteed. Starting even with a commutative generalized pseudo effect algebra, we can obtain a non-commutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz decomposition properties. We find conditions when kite pseudo effect algebras have the least non-trivial normal ideal.
pseudo effect algebra kite pseudo effect algebra generalized pseudo effect algebra riesz decomposition property normal ideal po-group strong unit lexicographic product subdirect irreducibility