Research Article

Norm-Compatible Fuzzy Subrings and Quotient Rings

Number: 55 June 30, 2026

Norm-Compatible Fuzzy Subrings and Quotient Rings

Abstract

In the study of fuzzy normed rings, classical frameworks frequently employ idempotent t-norms and t-conorms to govern the underlying algebraic operations. This paper investigates norm-induced fuzzy structures, in which the membership degree is defined by a strictly decreasing and continuous function of the underlying seminorm, and demonstrates an algebraic incompatibility. We prove that the direct application of idempotent operators limits the entire structure to bounded elements within the unit ball. This topological collapse prohibits the multiplicative norm expansion required to model unbounded systems, such as general polynomial or matrix rings. To address this, we introduce a norm-compatibility condition based on strict Archimedean t-norms. Building on this foundation, we construct the fuzzy quotient norm using norm-induced subrings and prove the First Isomorphism Theorem for fuzzy normed rings, thereby establishing that the isometric isomorphism holds without restricting the metric properties of the base ring.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory, Group Theory and Generalisations, Pure Mathematics (Other)

Journal Section

Research Article

Publication Date

June 30, 2026

Submission Date

March 30, 2026

Acceptance Date

June 19, 2026

Published in Issue

Year 2026 Number: 55

APA
Emniyet, A. (2026). Norm-Compatible Fuzzy Subrings and Quotient Rings. Journal of New Theory, 55, 58-66. https://doi.org/10.53570/jnt.1919557
AMA
1.Emniyet A. Norm-Compatible Fuzzy Subrings and Quotient Rings. JNT. 2026;(55):58-66. doi:10.53570/jnt.1919557
Chicago
Emniyet, Aykut. 2026. “Norm-Compatible Fuzzy Subrings and Quotient Rings”. Journal of New Theory, nos. 55: 58-66. https://doi.org/10.53570/jnt.1919557.
EndNote
Emniyet A (June 1, 2026) Norm-Compatible Fuzzy Subrings and Quotient Rings. Journal of New Theory 55 58–66.
IEEE
[1]A. Emniyet, “Norm-Compatible Fuzzy Subrings and Quotient Rings”, JNT, no. 55, pp. 58–66, June 2026, doi: 10.53570/jnt.1919557.
ISNAD
Emniyet, Aykut. “Norm-Compatible Fuzzy Subrings and Quotient Rings”. Journal of New Theory. 55 (June 1, 2026): 58-66. https://doi.org/10.53570/jnt.1919557.
JAMA
1.Emniyet A. Norm-Compatible Fuzzy Subrings and Quotient Rings. JNT. 2026;:58–66.
MLA
Emniyet, Aykut. “Norm-Compatible Fuzzy Subrings and Quotient Rings”. Journal of New Theory, no. 55, June 2026, pp. 58-66, doi:10.53570/jnt.1919557.
Vancouver
1.Aykut Emniyet. Norm-Compatible Fuzzy Subrings and Quotient Rings. JNT. 2026 Jun. 1;(55):58-66. doi:10.53570/jnt.1919557

 

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