(a, b)-Fuzzy subrings and (a, b)-fuzzy ideals of a ring

Document Type : Research Paper

Authors

1 Department of Mathematics, Dr.Vitthalrao Vikhe Patil College of Engineering,Ahmednagar 414001, India

2 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India

Abstract

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 called
an (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.

Keywords

References

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Journal of Hyperstructures
Volume 9, Issue 2
December 2020
Pages 96-114

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