Abstract Algebra: Theory and Applications · Problem 20

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · isomorphism-theorems-rings

Problem

Prove the Second Isomorphism Theorem for rings: Let

I

be a subring of a ring

R

and

J

an ideal in

R

. Then

I \cap J

is an ideal in

I

and

I/I \cap J \cong I + J/J.