Abstract
This study introduces the concept of hyperZ-algebra and investigates its features. In addition, we establish and prove a number of theorems about the relation between (Ṟ-ḧZ , Ḉ-ḧZ , Ḓ-ḧZ , Ṱ-ḧZ , Ṿ-ḧZ ). Moreover, we explain the hyper subalgebra ,a weakhyper Z-ideal and a stronghyper Z-ideal, as well as their relationship. Finally, the hyperhomomorphism Z-algebra is constructed and the isomorphism theorems are examined.
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