AAR12

From Exampleproblems

Let $x\,$ be a nilpotent element of the commutative ring $R\,$ . Let $x^m=0\,$ for minimal $m\isin \mathbb{Z}^+\,$ . Prove that $rx\,$ is nilpotent for all $r\isin R\,$ .

$(rx)^m=r^mx^m=r^m\cdot 0=0\,$

Main Page : Abstract Algebra : Rings

AAR12

From Exampleproblems

Views

Personal tools

Example problems .com

Search

Toolbox