A representation of weak effect algebras
Effect algebras [\textit{ {D.~J. Foulis}} and \textit{ {M.~K. Bennett}}, Found. Phys. 24, No. 10, 1331--1352 (1994; Zbl 1213.06004)] are partial algebras which play a significant role in the theory of partially ordered abelian groups. To overcome the problems that a partial operation implies for the applicability of universal-algebraic methods, the author, \textit{ {R. Halaš}} and \textit{ {J. Kühr}} have introduced in [Algebra Univers. 61, No. 2, 139--150 (2009; Zbl 1192.03048)] a way to extend the partial addition to a total one, being led to so-called weak basic algebras. Concerning the converse direction, however, a weak basic algebra does not in general give rise to an effect algebra. The present paper focusses for this reason on weak effect algebras, which generalise effect algebras and should not be mixed with the partial algebras studied by the reviewer in [\textit{ {T. Vetterlein}}, J. Electr. Eng. 54, No. 12/s, 61--64 (2003; Zbl 1062.03065)] under the same name. A mutual correspondence between weak effect algebras and weak basic algebras is established.
scientific article; zbMATH DE number 6072856