# Infinite ring with exactly two non trivial maximal ideals

Hey!

Is there an infinite ring with exactly two maximal ideals.

LiKeMath

Related Linear and Abstract Algebra News on Phys.org
What about $\mathbb{R}\times\mathbb{R}$?

Erland
What about $\mathbb{R}\times\mathbb{R}$?
How is multiplication defined here?

How is multiplication defined here?
Pointswise: $(a,b)\cdot (c,d)=(ac,bd)$.

mathwonk