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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: Let $ C$ be a finite field and let $ {C_m}$ denote the ring consisting of all $ m \times m$ matrices over $ C$. By a polynomial, we mean a polynomial in noncommuting indeterminates with coefficients in $ C$. It is shown here that a subset $ A$ of $ {C_m}$ is the range of a polynomial without constant term if and only if $ 0 \in A$ and $ uA{u^{ - 1}} \subseteq A$ for all invertible elements $ u \in {C_m}$.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1027090-3
Keywords: Polynomial, central polynomial, finite field
Article copyright: © Copyright 1990 American Mathematical Society