Answer to Question #50487 in Abstract Algebra for mathsstd

Question

Q. Let A and B be two ideals of ring R such that R=A⊕B show that R/A ≅B (R factor A is isomorphic to B) and
R/B ≅A (R factor B is isomorphic to A).

Answer 1

The set A / B is an ideal of the quotient R / B and the quotient ring (R / B) / (A / B) is isomorphic to R / A.