On ranges of polynomials in finite matrix rings

Author:
Chen-Lian Chuang

Journal:
Proc. Amer. Math. Soc. **110** (1990), 293-302

MSC:
Primary 16A38; Secondary 16A42, 16A44

DOI:
https://doi.org/10.1090/S0002-9939-1990-1027090-3

MathSciNet review:
1027090

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite field and let denote the ring consisting of all matrices over . By a polynomial, we mean a polynomial in noncommuting indeterminates with coefficients in . It is shown here that a subset of is the range of a polynomial without constant term if and only if and for all invertible elements .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1027090-3

Keywords:
Polynomial,
central polynomial,
finite field

Article copyright:
© Copyright 1990
American Mathematical Society