APM  Vol.4 No.9 , September 2014
On Finite Rank Operators on Centrally Closed Semiprime Rings
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.
Cite this paper: Cabello, J. , Casas, R. and Montiel, P. (2014) On Finite Rank Operators on Centrally Closed Semiprime Rings. Advances in Pure Mathematics, 4, 499-505. doi: 10.4236/apm.2014.49056.

[1]   Martindale 3rd, W.S. (1969) Prime Rings Satisfying a Generalized Polynomial Identity. Journal of Algebra, 12, 576-584.

[2]   Amitsur, S.A. (1972) On Rings of Quotiens. Symposia Mathematica, 8, 149-164.

[3]   Bresar, M., Chebotar, M.A. and MartindalWe III, W.S. (2007) Functional Identities. Birkhauser Verlag, Basel-Boston-Berlin.

[4]   Beidar, K.I., Martindale III, W.S. and Mikhalev, A.V. (1996) Rings with Generalized Identities. Marcel Dekker, New York.

[5]   Cabello, J.C., Cabrera, M., Rodríguez, A. and Roura, R. (2013) A Characterization of π-Complemented Rings. Communications in Algebra, 41, 3067-3079.