On Finite Rank Operators on Centrally Closed Semiprime Rings ()
J. C. Cabello,
R. Casas,
P. Montiel
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.
DOI: 10.4236/apm.2014.49056
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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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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