On pseudo BH-algebras

Abstract

As a generalization of $BH$-algebras, the notion of pseudo $BH$-algebra is introduced, and some of their properties are investigated. The notions of pseudo ideals, pseudo atoms, pseudo strong ideals, and pseudo homomorphisms in pseudo $BH$-algebras are introduced. Characterizations of their properties are provided. We show that every pseudo homomorphic image and preimage of a pseudo ideal is also a pseudo ideal. Any pseudo ideal of a pseudo $BH$-algebra can be decomposed into the union of some sets. The notion of pseudo complicated $BH$-algebra is introduced and some related properties are obtained.