TITLE:
On Finite Rank Operators on Centrally Closed Semiprime Rings
AUTHORS:
J. C. Cabello, R. Casas, P. Montiel
KEYWORDS:
Ring, Semiprime Ring, Extended Centroid, Minimal Idempotent
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.9,
September
4,
2014
ABSTRACT: We prove that the multiplication ring of a centrally closed semiprime ring R has a finite rank operator over the extended centroid C iff R contains an idempotent q such that qRq is finitely generated over C and, for each , there exist and e an idempotent of C such that xz=eq.