Some Properties of Hyper Ideals in Hyper Hoop‐Algebras

In this paper, we investigate the structural properties of hyper ideals in hyper hoop‐algebras, a generalization of hoop‐algebras under the framework of hyperstructures. Building upon foundational concepts in hyper group theory and hoop theory, the study introduces definitions for hyper ideals and weak hyper ideals, as well as their absorptive and implicative variants. Various properties, examples, and characterizations of these ideals are presented. Additionally, the paper explores quotient structures and homomorphisms in the context of hyper hoop‐algebras, and establishes connections between different classes of ideals through a series of theorems. These results extend classical ideal theory and provide new insights into the algebraic structure and logic of hyper hoop‐algebras.