Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0376713
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] G. Almkvist, Endomorphisms of finitely generated projective modules over a commutative ring, Ark. Mat. 11 (1973), 263-301. MR 0424786 (54:12744)
  • [2] N. Bourbaki, Éléments de mathématique. VII: Les structures fondamentales de l'analyse. Fasc. VII. Livre II: Algèbre. Chap. 3: Algèbre multilinéaire, Actualités Sci. Indust., no. 1044, Hermann, Paris, 1948. MR 10, 231. MR 0026989 (10:231d)
  • [3] T. Kløve, Linear recurring sequences in Boolean rings, Math. Scand. 33 (1973), 5-12. MR 0335387 (49:169)
  • [4] J. Mykkeltveit and E. S. Selmer, Linear recurrence in Boolean rings. Proof of Kløve's conjecture, Math. Scand. 33 (1973), 13-17. MR 0335388 (49:170)
  • [5] J. G. Rosenstein, On $ {\operatorname{GL} _2}(R)$ where $ R$ is a Boolean ring, Canad. Math. Bull. 15 (1972), 263-275. MR 46 #3637. MR 0304502 (46:3637)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A33

Retrieve articles in all journals with MSC: 15A33

Additional Information

Keywords: Boolean ring, recursive sequence, trace, exterior powers, primitive polynomial, exponent
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society