Semicommutative property on nilpotent products. (Q2929760)

A ring \(R\) is called nil-semicommutative if for every \(a,b\in R\), \(ab\in N(R)\) implies \(arb\in N(R)\) for every \(r\in R\), where \(N(R)\) is the set of all nilpotent elements in \(R\). In this paper the authors describe many interesting properties of nil-semicommutative rings and show their connections with some important classes of rings such as Armendaritz rings or von Neuman regular rings, for example. They investigate the structure of Ore extensions when upper nilradicals are \(\sigma\)-rigid \(\delta\)-ideals. Moreover, they examine 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.