New determinants and the CayleyHamilton theorem for matrices over Lie nilpotent rings
Author:
Jeno Szigeti
Journal:
Proc. Amer. Math. Soc. 125 (1997), 22452254
MSC (1991):
Primary 16A38, 15A15; Secondary 15A33
MathSciNet review:
1389540
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Abstract: We construct the socalled 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 CayleyHamilton 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, MiskolcEgyetemváros, 3515 Hungary
Email:
matszj@gold.unimiskolc.hu
DOI:
http://dx.doi.org/10.1090/S0002993997038689
PII:
S 00029939(97)038689
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
