Abstract Algebra: Theory and Applications · Problem 22

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · correspondence-theorem-rings

Problem

Prove the Correspondence Theorem: Let

I

be an ideal of a ring

R

. Then

S \to S/I

is a one-to-one correspondence between the set of subrings

S

containing

I

and the set of subrings of

R/I

. Furthermore, the ideals of

R

correspond to ideals of

R/I