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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On reflexivity of direct sums


Authors: V. P. Camillo and K. R. Fuller
Journal: Proc. Amer. Math. Soc. 128 (2000), 2855-2862
MSC (1991): Primary 16D20, 16G99, 16P10; Secondary 47A15
Published electronically: April 28, 2000
MathSciNet review: 1664341
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Abstract:

Necessary and sufficient conditions are presented to insure that the direct sum of two reflexive representations of a finite dimensional algebra is reflexive, and it is shown that for each such algebra, there is an integer $ k $ such that the direct sum of $k$ copies of each of its representations is reflexive. Given a ring $\Delta ,$ our results are actually presented in the more general setting of $\Delta $-representations of a ring $R.$


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Additional Information

V. P. Camillo
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: camillo@math.uiowa.edu

K. R. Fuller
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: kfuller@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05331-4
PII: S 0002-9939(00)05331-4
Received by editor(s): September 10, 1998
Received by editor(s) in revised form: November 10, 1998
Published electronically: April 28, 2000
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society