What question did this study set out to answer?

The goal is to examine the properties and definitions of hyper ideals within hyper hoop-algebras.

January 20, 2026Open Access

Some Properties of Hyper Ideals in Hyper Hoop‐Algebras

Key Points

The goal is to examine the properties and definitions of hyper ideals within hyper hoop-algebras.
Introduction of definitions for hyper ideals and weak hyper ideals.
Investigation of absorptive and implicative variants of hyper ideals.
Exploration of quotient structures and homomorphisms.
Theoretical analysis and presentation of properties and examples.
Introduced new definitions that clarify the structure of hyper ideals.
Established connections between different classes of ideals through theorems.
Extended classical ideal theory within the scope of hyper hoop-algebras.

Abstract

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.

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