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.
References
[1]
Martindale 3rd, W.S. (1969) Prime Rings Satisfying a Generalized Polynomial Identity. Journal of Algebra, 12, 576-584. http://dx.doi.org/10.1016/0021-8693(69)90029-5
[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. http://dx.doi.org/10.1080/00927872.2012.672604
![\"\"](\"Edit_fdf88a1a-f823-483b-aef5-87577d062d48.bmp\")
, there exist ![\"\"](\"Edit_6c4e66c2-f711-439e-9b25-8fdc014a7e6c.bmp\")
and e an idempotent of C such that xz=eq.
