Some results on annihilation in algebras (Q790910)

Let R be an algebra over the field F, and L a nonzero left ideal. Define M(L) to be the set of \(a\in R\) which left-annihilate some power of each element of L; define G(L) to be the set of \(a\in R\) such that for each \(u\in L\), there exists a nonzero p(t)\(\in F[t]\) for which \(ap(u)=0\). It is proved that M(L)L is a nil left ideal, and G(L)L is an algebraic left ideal. These results extend earlier ones due to \textit{J. Bergen} and the author [J. Algebra 85, 217-242 (1983; Zbl 0526.16027)].