(a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring
As an extension of the concept of a fuzzy subring and a fuzzy ideal, a new kind of a fuzzy subring and a fuzzy ideal calledan (a, b)-fuzzy subring and an (a, b)-fuzzy ideal of a ring is defined and their properties are studied. We also investigate the preimage of an (a, b)-fuzzy subring and an (a, b...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Mohaghegh Ardabili
2020-12-01
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| Series: | Journal of Hyperstructures |
| Subjects: | |
| Online Access: | https://jhs.uma.ac.ir/article_2633_851a28e3f7e4fd078d0023416fcf807d.pdf |
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| Summary: | As an extension of the concept of a fuzzy subring and a fuzzy ideal, a new kind of a fuzzy subring and a fuzzy ideal calledan (a, b)-fuzzy subring and an (a, b)-fuzzy ideal of a ring is defined and their properties are studied. We also investigate the preimage of an (a, b)-fuzzy subring and an (a, b)-fuzzy ideal under a ring homomorphism. Also, (a, b)-level fuzzy subrings (fuzzy ideals) are studied. A necessary and sufficient condition for two (a, b)-level fuzzy subrings (fuzzy ideals) to be equal is proved. We show that the set of cosets of an (a, b)-fuzzy ideal forms a ring. |
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| ISSN: | 2251-8436 2322-1666 |