Theoretical models for constructing $H_v$-near fields

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Yazd University, Yazd, Iran

Abstract

In this paper, we introduce the notion of $H_v$-near fields as a new generalization of classical near fields within the framework of hyperstructure theory. The concept of an $H_v$-near field is introduced and defined here for the first time. The main contribution of this paper is the development of the foundational theory of $H_v$-near fields, including the investigation of their basic algebraic properties, structural characteristics, and construction methods. Several examples and construction techniques are presented to illustrate the existence and diversity of these hyperalgebraic structures. Furthermore, we define and study the fundamental relation $\theta^{*}$, which plays a central role in describing equivalence classes and the internal structure of $H_v$-near fields. Our approach is based on methods and techniques from hyperstructure theory.

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References

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Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 02 July 2026

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  • Receive Date: 16 November 2025
  • Revise Date: 16 June 2026
  • Accept Date: 28 June 2026

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