On Pseudo $BN$-algebras

In this paper, we introduce the notion of pseudo $BN$-algebras and investigate some of its basic properties. Moreover, its relationship with the already established pseudo $BF$-algebra is investigated. Furthermore, subalgebras, ideals and pseudo-normality of pseudo $BN$-algebras are studied. Illustrations are provided for new concepts. Finally, we establish the equivalency of pseudo-normal subalgebras and pseudo-normal ideals.