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SKEW POLYNOMIALS AND ALGEBRAIC REFLEXIVITY

Published online by Cambridge University Press:  01 May 2003

NICOLE SNASHALL  and
J. F. WATTERS
NICOLE SNASHALL
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, England
J. F. WATTERS
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, Leicester LE1 7RH, England
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Abstract

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For an arbitrary $K$-algebra $R$, an $R$, $K$-bimodule $M$ is algebraically reflexive if the only $K$-endomorphisms of $M$ leaving invariant every $R$-submodule of $M$ are the scalar multiplications by elements of $R$. Hadwin has shown for an infinite field $K$ and $R = K[x]$ that $R$ is reflexive as an $R$, $K$-bimodule. This paper provides a generalisation by giving a skew polynomial version of his result.

Keywords

Primary 16D2016S36
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 7 - 9
Copyright
2003 Glasgow Mathematical Journal Trust