Originally Posted by

**ThePerfectHacker** Let R be a commutative ring (with unity) that contains only two ideals, {0} and R. Let I be an ideal of R. If R is a ring such that $\displaystyle 1\not = 0$ (kalagota forgot to mention that) then choose $\displaystyle a\not = 0$. Now define $\displaystyle \left< a\right> = \{ ra|r\in R\}$. Then clearly this is an ideal of R and is non-trivial so it means $\displaystyle \left< a \right> = R$ which means there exists a $\displaystyle b$ so that $\displaystyle ab=1$. This shows all the non-zero elements of R has inverses, this makes R a field. Q.E.D.