Quotient Rings Induced via Intuitionistic Fuzzy Ideals

Abstract

This work we give a construction of a quotient ring $R/{<}\mu ,\nu {>}$ induced via an intuitionistic fuzzy ideal ${<}\mu ,\nu {>}$ 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 ${<}\mu ,\nu {>}$ is an intuitionistic fuzzy ideal of a commutative ring R, then ${<}\mu ,\nu {>}$ is prime (resp, primary) if and only if $R/{<}\mu ,\nu {>}$ is an integral domain (resp, every zero divisor in $R/{<}\mu ,\nu {>}$ is nilpotent).