On reflexivity of direct sums

Camillo, V.; Fuller, K.

doi:10.1090/S0002-9939-00-05331-4

On reflexivity of direct sums
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by V. P. Camillo and K. R. Fuller

Proc. Amer. Math. Soc. 128 (2000), 2855-2862

DOI: https://doi.org/10.1090/S0002-9939-00-05331-4

Published electronically: April 28, 2000

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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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