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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Powers of a matrix with coefficients in a Boolean ring


Author: Gert Almkvist
Journal: Proc. Amer. Math. Soc. 53 (1975), 27-31
MSC: Primary 15A33
DOI: https://doi.org/10.1090/S0002-9939-1975-0376713-2
MathSciNet review: 0376713
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Abstract: The best possible integer $ {u_n}$ such that $ {f^{{u_n}}} = 1$, if $ f$ is an invertible $ n \times n$ matrix with coefficients in a Boolean ring, is determined. The period of linear recursive sequences in a Boolean ring (e.g. the trace sequence $ \{ \operatorname{Tr} {f^k}\} _1^\infty $) is computed.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0376713-2
Keywords: Boolean ring, recursive sequence, trace, exterior powers, primitive polynomial, exponent
Article copyright: © Copyright 1975 American Mathematical Society