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Fuzzy Normed Rings

1
Department of Mathematics, Osmaniye Korkut Ata University, 8000 Osmaniye, Turkey
2
Department of Mathematics, Gaziantep University, 27310 Gaziantep, Turkey
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 515; https://doi.org/10.3390/sym10100515
Received: 12 September 2018 / Revised: 6 October 2018 / Accepted: 8 October 2018 / Published: 16 October 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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PDF [227 KB, uploaded 16 October 2018]

Abstract

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples. View Full-Text
Keywords: Fuzzy sets; ring; normed space; fuzzy normed ring; fuzzy normed ideal Fuzzy sets; ring; normed space; fuzzy normed ring; fuzzy normed ideal
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Emniyet, A.; Şahin, M. Fuzzy Normed Rings. Symmetry 2018, 10, 515.

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