| Abstract: | Abstract We define the lower socle of a semiprime algebra 𝒜 as the sum of all minimal left ideals 𝒜e where e is a minimal idempotent such that the division algebra e𝒜e is finite dimensional. We study the connection between the condition that the elements a k , b k , 1 ≤ k ≤ n, lie in the lower socle of 𝒜 and the condition that the elementary operator x ? a 1 xb 1 + ? + a n xb n has finite rank. As an application we obtain some results on derivations certain of whose powers have finite rank. |
