Fuzzy Normed Rings
Abstract
:1. Introduction
2. Preliminaries
- 1.
- ,
- 2.
- ,
- 3.
- , (and henceif identity exists), and
- 4.
- .
- (1)
- is commutative and associative, that is,and,
- (2)
- is continuous,
- (3)
- ,
- (4)
- is monotone, which meansif,
- (5)
- for, and
- (6)
- whenand,for all.
- (1)
- is commutative and associative, that is,and,
- (2)
- is continuous,
- (3)
- ,
- (4)
- is monotone, which meansif,
- (5)
- for, and
- (6)
- whenand,for all.
3. Fuzzy Normed Rings and Fuzzy Normed Ideals
- (i)
- (ii)
- .
- i.
- Letbe a fuzzy normed subring of the normed ringand letbe a ring homomorphism. Then,is a fuzzy normed subring of.
- ii.
- Letbe a normed ring homomorphism. Ifis a fuzzy normed subring of, thenis a fuzzy normed subring of.
- (i)
- and
- (ii)
- ,
- (i)
- and
- (ii)
- ,
- (i)
- ,
- (ii)
- ,
- (iii)
- and
- (iv)
- if 1 is the multiplicative identity of, then.
4. Fuzzy Normed Prime Ideal and Fuzzy Normed Maximal Ideal
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
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Emniyet, A.; Şahin, M. Fuzzy Normed Rings. Symmetry 2018, 10, 515. https://doi.org/10.3390/sym10100515
Emniyet A, Şahin M. Fuzzy Normed Rings. Symmetry. 2018; 10(10):515. https://doi.org/10.3390/sym10100515
Chicago/Turabian StyleEmniyet, Aykut, and Memet Şahin. 2018. "Fuzzy Normed Rings" Symmetry 10, no. 10: 515. https://doi.org/10.3390/sym10100515