Quotient Rings Induced via Intuitionistic Fuzzy Ideals

摘要

This work we give a construction of a quotient ring R/<μ, v> induced via an intuitionistic fuzzy ideal <μ, v> in a ring R. The Intuitionistic Fuzzy First, Second and Third Isomorphism Theorems are established. For some applications of this construction of quotient rings, we show that if <μ, v> is an intuitionistic fuzzy ideal of a commutative ring R, then <μ, v> is prime (resp, primary) if and only if R/<μ, v> is an integral domain (resp, every zero divisor in R/<μ, v> is nilpotent).