Let \(R\) be a commutative ring with 1, \(I,J\) ideals such that \(I+J=R\). Show that \(R/(IJ)\cong R/I\oplus R/J\).
Question
Math 6310 • Algebra
Fall 2005 • Question 3
Question
Fall 2005 • Question 3
Let \(R\) be a commutative ring with 1, \(I,J\) ideals such that \(I+J=R\). Show that \(R/(IJ)\cong R/I\oplus R/J\).