On Finite Rank Operators on Centrally Closed Semiprime Rings
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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.
Keywords:
Ring,
Semiprime Ring,
Extended Centroid,
Minimal Idempotent
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.
References
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