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On Finite Rank Operators on Centrally Closed Semiprime Rings
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
- 1 Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Granada, Spain
- 2 Departamento de Didáctica de las Ciencias Experimentales, Facultad de Ciencias de la Educación, Universidad de Granada, Granada, Spain
- 3 Departamento de Matemáticas, Centro de Magisterio La Inmaculada, Universidad de Granada, Granada, Spain
Advances in Pure Mathematics·Volume 04 (2014)·Pages 499–505·Published 4 September 2014·DOI10.4236/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.
KeywordsRingSemiprime RingExtended CentroidMinimal Idempotent
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