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Proceedings of the American Mathematical Society

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Countable linear transformations are clean


Authors: W. K. Nicholson and K. Varadarajan
Journal: Proc. Amer. Math. Soc. 126 (1998), 61-64
MSC (1991): Primary 16S50; Secondary 16E50, 16U99
DOI: https://doi.org/10.1090/S0002-9939-98-04397-4
MathSciNet review: 1452816
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Abstract: It is shown that every linear transformation on a vector space of countable dimension is the sum of a unit and an idempotent.


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Additional Information

W. K. Nicholson
Affiliation: Department of Mathematics, University of Calgary, Calgary, Canada T2N 1N4
Email: wknichol@acs.ucalgary.ca

K. Varadarajan
Affiliation: Department of Mathematics, University of Calgary, Calgary, Canada T2N 1N4
Email: varadara@math.ucalgary.ca

DOI: https://doi.org/10.1090/S0002-9939-98-04397-4
Keywords: Clean rings, vector space endomorphism rings, unit regular rings.
Received by editor(s): July 16, 1996
Additional Notes: This work was supported by NSERC grants A8075 and A8225
Communicated by: Ken Goodearl
Article copyright: © Copyright 1998 American Mathematical Society