Pseudo GE-Algebras as the Extension of GE-Algebras

Abstract

In this paper, the notion of a pseudo GE-algebra as an extension of a GE-algebra is introduced. Basic properties of pseudo GE-algebras are described. The concepts of strong pseudo BE-algebra, good pseudo BE-algebra, good pseudo GE-algebra, and the relationship between them are established. We provide a condition for a good pseudo BE-algebra to be a pseudo GE-algebra and for a strong pseudo BE-algebra to be a pseudo GE-algebra.