Abstract Algebra: Theory and Applications · Problem 21

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · isomorphism-theorems-rings

Problem

Prove the Third Isomorphism Theorem for rings: Let

R

be a ring and

I

and

J

be ideals of

R

, where

J \subset I

. Then

R/I \cong \frac{R/J}{I/J}.