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On Finite Rank Operators on Centrally Closed Semiprime Rings

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DOI: 10.4236/apm.2014.49056    2,209 Downloads   2,583 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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