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New determinants and the Cayley-Hamilton theorem for matrices over Lie nilpotent rings

Author: Jeno Szigeti
Journal: Proc. Amer. Math. Soc. 125 (1997), 2245-2254
MSC (1991): Primary 16A38, 15A15; Secondary 15A33
MathSciNet review: 1389540
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Abstract: We construct the so-called right adjoint sequence of an $n\times n$ matrix over an arbitrary ring. For an integer $m\geq 1$ the right $m$-adjoint and the right $m$-determinant of a matrix is defined by the use of this sequence. Over $m$-Lie nilpotent rings a considerable part of the classical determinant theory, including the Cayley-Hamilton theorem, can be reformulated for our right adjoints and determinants. The new theory is then applied to derive the PI of algebraicity for matrices over the Grassmann algebra.

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Additional Information

Jeno Szigeti
Affiliation: Institute of Mathematics, University of Miskolc, Miskolc-Egyetemváros, 3515 Hungary

Received by editor(s): December 19, 1995
Received by editor(s) in revised form: March 6, 1996
Additional Notes: Supported by OTKA of Hungary, grant no. T7558, and by the Computer and Automation Institute of the Hungarian Academy of Science.
Communicated by: Lance W. Small
Article copyright: © Copyright 1997 American Mathematical Society

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