Let \(I\) be the ideal \((2,1+\sqrt {-5})\) in the ring \(R := \mathbb {Z}[\sqrt {-5}]\). Prove that \(I\otimes _R I\) is isomorphic to \(2R\).
Question
Math 6310 • Algebra
Spring 2026 • Question 3
Question
Spring 2026 • Question 3
Let \(I\) be the ideal \((2,1+\sqrt {-5})\) in the ring \(R := \mathbb {Z}[\sqrt {-5}]\). Prove that \(I\otimes _R I\) is isomorphic to \(2R\).