Pre-Hilbert Algebras with Condition (GE3)

Abstract

GE-algebras are introduced as a generalization of Hilbert algebras in 2020. In this paper, we show that a self distributive GE-algebra is equivalent to the pimpl-RML algebra, and a transitive GE algebra is equivalent to the pi-pre-BBBCC algebra with condition (An). Further, we prove that pimpl-BE algebras are a subclass of pimpl-RML algebras and pre-Hilbert algebras with condition (GE3) are equivalent to the pi-pre-BBBCC algebras with condition (An).