Let \(R\) be a commutative ring with 1. Suppose \(I\) and \(J\) are two ideals of \(R\) such that \(I+J=R\). Prove that \(R/(IJ)\cong R/I\oplus R/J\).
Question
Math 6310 • Algebra
Spring 2007 • Question 7
Question
Spring 2007 • Question 7
Let \(R\) be a commutative ring with 1. Suppose \(I\) and \(J\) are two ideals of \(R\) such that \(I+J=R\). Prove that \(R/(IJ)\cong R/I\oplus R/J\).