Fuzzy Normed Rings
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 norme...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-10-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2073-8994/10/10/515 |
| _version_ | 1798002534513639424 |
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| author | Aykut Emniyet Memet Şahin |
| author_facet | Aykut Emniyet Memet Şahin |
| author_sort | Aykut Emniyet |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:53:42Z |
| format | Article |
| id | doaj.art-fa9b6c2adfce40ce97e57445f8073cdb |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T11:53:42Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fa9b6c2adfce40ce97e57445f8073cdb2022-12-22T04:25:14ZengMDPI AGSymmetry2073-89942018-10-01101051510.3390/sym10100515sym10100515Fuzzy Normed RingsAykut Emniyet0Memet Şahin1Department of Mathematics, Osmaniye Korkut Ata University, 8000 Osmaniye, TurkeyDepartment of Mathematics, Gaziantep University, 27310 Gaziantep, TurkeyIn 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.http://www.mdpi.com/2073-8994/10/10/515Fuzzy setsringnormed spacefuzzy normed ringfuzzy normed ideal |
| spellingShingle | Aykut Emniyet Memet Şahin Fuzzy Normed Rings Symmetry Fuzzy sets ring normed space fuzzy normed ring fuzzy normed ideal |
| title | Fuzzy Normed Rings |
| title_full | Fuzzy Normed Rings |
| title_fullStr | Fuzzy Normed Rings |
| title_full_unstemmed | Fuzzy Normed Rings |
| title_short | Fuzzy Normed Rings |
| title_sort | fuzzy normed rings |
| topic | Fuzzy sets ring normed space fuzzy normed ring fuzzy normed ideal |
| url | http://www.mdpi.com/2073-8994/10/10/515 |
| work_keys_str_mv | AT aykutemniyet fuzzynormedrings AT memetsahin fuzzynormedrings |