School of Science, Jiangnan University, Wuxi, China

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Abstract—Our aim in this paper is to introduce and study the new type of fuzzy subrings of a ring called fuzzy (resp. completely, weakly) regular subring, generalized fuzzy (resp. completely , weakly ) regular subring, (∈,∈∨q_(λ,μ))-Fuzzy ( resp. completely , weakly ) regular subring and the direct products of them .Some of their algebraic properties are characterized by their level sets and extension principle. Finally, we give the properties of homomorphic image and homomorphic preimage of them.

Index Terms—(∈,∈∨q_( λ ,μ))-Fuzzy  subrings; generalized fuzzy subrings; homomorphic image; homomorphic preimage; level set; direct product

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Cite: Zuhua Liao, Shu Cao, Miaohan Hu and Lian Wu, "(∈,∈∨q_(λ,μ))-Fuzzy Regular Subrings," Journal of Computers vol. 7, no. 2, pp. 483-490, 2012.