Affiliations: [a] Research and Development Centre, Bharathiar University, Coimbatore, India | [b] Department of Mathematics, Perunthalaivar Kamarajar Institute of Engineering and Technology, Karaikal, India | [c] Department of Mathematics, Annamalai University, Annamalainagar, India
Correspondence:
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Corresponding author. P. Nandakumar, Department of Mathematics, Perunthalaivar Kamarajar Institute of Engineering and Technology, Karaikal-609603, India. Tel.: +91 9444290545; Fax: +04368 262234; E-mail: [email protected].
Abstract: In this study, using Yuan and Lee’s definition of fuzzy group based on fuzzy binary operation and Aktas and Cagman definition of fuzzy ring, we give a new kind of definition to (A : B). The concept of fuzzy regular and fuzzy left strongly regular are introduced and we create a new study on their basic properties equivalent to those of ordinary rings. We have shown that if (R, G, H) is strongly regular, then for any a ∈ R, left annihilator of “a” is an ideal.
Keywords: Ring theory, regular rings, ideals, fuzzy algebraic structures
