A ring in which all prime ideals are maximal
Let
View code
Let $R$ be a commutative ring with identity. Suppose that for every $a\in R$ there is an integer $n\geq 2$ such that $a^n=a$. Show that every prime ideal of $R$ is maximal.
Let
Let $R$ be a commutative ring with identity. Suppose that for every $a\in R$ there is an integer $n\geq 2$ such that $a^n=a$. Show that every prime ideal of $R$ is maximal.