Let \(m,n\) be positive integers and \(d\) their greatest common divisor. Show that \[ \mathbb {Z}/m\mathbb {Z}\otimes _{\mathbb {Z}}\mathbb {Z}/n\mathbb {Z}\cong \mathbb {Z}/d\mathbb {Z}. \]
Question
Math 6310 • Algebra
Spring 2011 • Question 7
Question
Spring 2011 • Question 7
Let \(m,n\) be positive integers and \(d\) their greatest common divisor. Show that \[ \mathbb {Z}/m\mathbb {Z}\otimes _{\mathbb {Z}}\mathbb {Z}/n\mathbb {Z}\cong \mathbb {Z}/d\mathbb {Z}. \]