“School of Mathematics”
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| Paper IPM / M / 8681 |
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| Abstract: | |
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Let D be a division ring, V a right or left vector
space over D, and L(V) the ring of all right
(resp. left) linear transformations on V. We characterize
certain one-sided ideals of the ring L(V) in
terms of their rank-one idempotents. We use our result to
characterize a division ring D in terms of the one-sided ideals of
Mn(D). Some other consequences are presented.
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