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 matrix over an arbitrary ring. For an integer the right -adjoint and the right -determinant of a matrix is defined by the use of this sequence. Over -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

Email:
matszj@gold.uni-miskolc.hu

DOI:
https://doi.org/10.1090/S0002-9939-97-03868-9

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