Journal of the
Korean Mathematical Society JKMS

The semicommutative property of rings was introduced initially by Bell, and has done important roles in noncommutative ring theory. This concept was generalized to one of {\it nil-semicommutative} by Chen. We first study some basic properties of nil-semicommutative rings. We next investigate the structure of Ore extensions when upper nilradicals are $\sigma$-rigid $\delta$-ideals, examining the nil-semicommutative ring property of Ore extensions and skew power series rings, where $\sigma$ is a ring endomorphism and $\delta$ is a $\sigma$-derivation.

Keywords: (nil-)semicommutative ring, NI ring, polynomial ring, Ore extension, skew power series ring

MSC numbers: 16U80, 16N40