On Finite Rank Operators on Centrally Closed Semiprime Rings
Affiliation(s)
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain. Departamento de Didáctica de las Ciencias Experimentales, Facultad de Ciencias de la Educación, Universidad de Granada, Granada, Spain. Departamento de Matemáticas, Centro de Magisterio La Inmaculada, Universidad de Granada, Granada, Spain.
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain. Departamento de Didáctica de las Ciencias Experimentales, Facultad de Ciencias de la Educación, Universidad de Granada, Granada, Spain. Departamento de Matemáticas, Centro de Magisterio La Inmaculada, Universidad de Granada, Granada, Spain.
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.
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.
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.
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
[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