Theorem

Semicommutative rings from Armendariz rings

If $R$ is Armendariz, and $N$ is a nil one-sided ideal of $R$, then $Z(R)+N$ is semicommutative and Armendariz.

Reference(s)

  • C. Huh, Y. Lee, and A. Smoktunowicz. Armendariz rings and semicommutative rings. (2002) @ Corollary 9, p 756