Hyper Ideals in Hyper Equality Algebras

In this paper, the concept of (strong) hyper ideals in bounded hyper equality algebras which is a generalization of ideals in bounded equality algebras are introduced. Also, the relations between strong hyper ideals and hyper deductive systems in good bounded hyper equality algebras are studied and in the follow, the notion of involutive hyper equality algebras are introduced. Moreover, A regular hyper congruence relation via a strong hyper ideal in good involutive hyper equality algebras are constructed and finally, the quotient hyper equality algebras via hyper strong hyper ideals are provided.

Keywords:

(Involutive) Hyper equality algebra , (strong , weak) hyper ideal , hyper congruence.