Results on hyper equality algebras

Abstract

Equality algebras as a generalization of EQ-algebras introduced by Jenei [8]. Hyper equal- ity algebras introduced and studied in [4], as a generalization of equality algebras. Now, in this paper, we investigate relations among hyper equality algebras and other hyper algebraic structures such as hyper K(BE, MV)-algebras and hyper hoops. Specially, we prove that any linearly ordered hyper MV-algebra is a strongly commutative symmetric hyper equality algebra and under some conditions, any strongly commutative involutive hyper equality algebra is a hyper MV-algebra.