Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields

Takaaki Fujita

doi:10.63673/SJS.1850268

Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields

Abstract

Mathematical structures can be extended to hyperstructures and 𝑛-superhyperstructures by leveraging the powerset and its 𝑛-fold iteration (cf. [1]). These generalized frameworks are particularly well suited for modeling hierarchical relationships across diverse domains. In this paper, we examine the hyperfield and superhyperfield introduced in [2]. Recall that a field is an algebraic structure (𝐹, +, ·) in which (𝐹, +) and (𝐹 \ {0}, ·) are commutative groups and multiplication distributes over addition. A hyperfield generalizes this by replacing addition with a hyperaddition that maps each pair of elements to a subset of 𝐹, while preserving a commutative multiplicative group and distributivity. A superhyperfield further extends a hyperfield by lifting its operations to iterated powersets, yielding multi-level hyperaddition and multiplication structures.

Keywords

Supporting Institution

This study did not receive any financial or external support from organizations or individuals.

Ethical Statement

As this research is entirely theoretical in nature and does not involve human participants or animal subjects, no ethical approval is required.

Thanks

We extend our sincere gratitude to everyone who provided insights, inspiration, and assistance throughout this research. We particularly thank our readers for their interest and acknowledge the authors of the cited works for laying the foundation that made our study possible. We also appreciate the support from individuals and institutions that provided the resources and infrastructure needed to produce and share this paper. Finally, we are grateful to all those who supported us in various ways during this project.

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Details

Primary Language

English

Subjects

Statistics (Other), Applied Mathematics (Other)

Journal Section

Research Article

Authors

Takaaki Fujita ^*
0009-0007-1509-2728
Japan

Publication Date

May 12, 2026

Submission Date

December 27, 2025

Acceptance Date

March 4, 2026

Published in Issue

Year 2026 Volume: 52 Number: 1

DOI

https://doi.org/10.63673/SJS.1850268

IZ

https://izlik.org/JA23UP26ZS

Cite

RIS / Bibtex

APA

Fujita, T. (2026). Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields. Selcuk Journal of Science, 52(1), 40-59. https://doi.org/10.63673/SJS.1850268

AMA

1.Fujita T. Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields. Selcuk J. Sci. 2026;52(1):40-59. doi:10.63673/SJS.1850268

Chicago

Fujita, Takaaki. 2026. “Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields”. Selcuk Journal of Science 52 (1): 40-59. https://doi.org/10.63673/SJS.1850268.

EndNote

Fujita T (May 1, 2026) Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields. Selcuk Journal of Science 52 1 40–59.

IEEE

[1]T. Fujita, “Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields”, Selcuk J. Sci., vol. 52, no. 1, pp. 40–59, May 2026, doi: 10.63673/SJS.1850268.

ISNAD

Fujita, Takaaki. “Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields”. Selcuk Journal of Science 52/1 (May 1, 2026): 40-59. https://doi.org/10.63673/SJS.1850268.

JAMA

1.Fujita T. Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields. Selcuk J. Sci. 2026;52:40–59.

MLA

Fujita, Takaaki. “Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields”. Selcuk Journal of Science, vol. 52, no. 1, May 2026, pp. 40-59, doi:10.63673/SJS.1850268.

Vancouver

1.Takaaki Fujita. Multi-Level Algebraic Systems: A Study of Hyperfields and Superhyperfields. Selcuk J. Sci. 2026 May 1;52(1):40-59. doi:10.63673/SJS.1850268