Ideals and filters in pseudo-effect algebras
In his thesis of 2003, Jing proved that, in a pseudo-effect algebra, an ideal is always a local ideal and that a filter is always a local filter. On the other hand, \textit{Y. Shang} and \textit{Y. Li} introduced in [Int. J. Theor. Phys. 42, No. 12, 2823--2829 (2003; Zbl 1037.81007)] the notion of a generalized ideal and proved that it is equivalent to the notion of an ideal. In the paper under review, the authors show that, just as in effect algebras, every local ideal (local filter) in a pseudo-effect algebra is an ideal (resp., filter) and that the notions of generalized ideal and ideal are equivalent also in pseudo-effect algebras. Their methods rest on the left and right subtraction operations on pseudo-effect algebras introduced by them in a recent paper [Int. J. Theor. Phys. 43, No. 6, 1453--1460 (2004; Zbl 1073.81011), reviewed below].
scientific article; zbMATH DE number 2146155