Commutativity conditions on derivations and Lie ideals $\sigma$-prime rings
Commutativity conditions on derivations and Lie ideals $\sigma$-prime rings
Let $R$ be a 2-torsion free $\sigma$-prime ring, $U$ a nonzero square closed $\sigma$-Lie ideal of $R$ and let $d$ be a derivation of $R$. In this paper it is shown that: 1) If $d$ is centralizing on $U$, then $d = 0$ or $U \subseteq Z(R)$. 2) If either $d([x, y]) = 0$ for all $x, y \in U$, or $[d(x), d(y)] = 0$ for all $x, y \in U$ and $d$ commutes with $\sigma$ on $U$, then $d = 0$ or $U \subseteq Z(R)$.
Comment: 9 pages
Prime and semiprime associative rings, \(\sigma\)-prime rings, Rings with involution; Lie, Jordan and other nonassociative structures, centralizing derivations, Generalizations of commutativity (associative rings and algebras), Lie ideals, Mathematics - Rings and Algebras, Derivations, actions of Lie algebras, commutativity theorems, Center, normalizer (invariant elements) (associative rings and algebras), 16W10, 16W25, 16U80
Prime and semiprime associative rings, \(\sigma\)-prime rings, Rings with involution; Lie, Jordan and other nonassociative structures, centralizing derivations, Generalizations of commutativity (associative rings and algebras), Lie ideals, Mathematics - Rings and Algebras, Derivations, actions of Lie algebras, commutativity theorems, Center, normalizer (invariant elements) (associative rings and algebras), 16W10, 16W25, 16U80
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!