On double basic algebras and pseudo-effect algebras
Double basic algebras have been introduced in [\textit{I. Chajda}, ``Double basic algebras'', Order 26, No. 2, 149--162 (2009; Zbl 1173.06002)] as a counterpart of bounded lattices with order-antiautomorphisms on principal filters. Now their independent axiomatization is given. Double basic algebras represent a non-commutative extension of basic algebras which generalize orthomodular lattices in a similar way as MV-algebras generalize Boolean algebras. Lattice pseudo-effect algebras are characterized as a subvariety of double basic algebras and pairs of compatible elements of lattice pseudo-effect algebras are described in terms of double basic algebras.
scientific article; zbMATH DE number 5988081