SHARP ELEMENTS IN d۰-ALGEBRAS

We introduce the notions of Sasaki mapping and of sharp elements on a d۰-algebra. We investigate the relationships of sharp elements with Sasaki mappings and with central elements, thus generalizing some results known for D-lattices. Namely, we give a characterization of sharp elements, by means of Sasaki mappings, which extends a result of Bennett and Foulis; we also prove that an element is central if and only if it is a sharp element and every element is compatible with it: this generalizes a result of Riecanová.

کلیدواژه ها:

BCK-algebra ، D-lattice ، effect algebra ، orthomodular lattice ، Sasaki mapping ، central element