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NOETHER NUMBERS FOR SUBREPRESENTATIONS OF CYCLIC GROUPS OF PRIME ORDER

Published online by Cambridge University Press:  24 March 2003

R. JAMES SHANK
Affiliation:
Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury CT2 7NF [email protected]
DAVID L. WEHLAU
Affiliation:
Department of Mathematics and Computer Science, Royal Military College, Kingston, Ontario, Canada K7K 7B4 [email protected]
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Abstract

Let $W$ be a finite-dimensional ${\bb Z}/p$ -module over a field, ${\bf k}$ , of characteristic $p$ . The maximum degree of an indecomposable element of the algebra of invariants, ${\bf k}[W]^{{\bb Z}/p}$ , is called the Noether number of the representation, and is denoted by $\beta(W)$ . A lower bound for $\beta(W)$ is derived, and it is shown that if $U$ is a ${\bb Z}/p$ submodule of $W$ , then $\beta(U)\le \beta(W)$ . A set of generators, in fact a SAGBI basis, is constructed for ${\bf k}[V_2\oplus V_3]^{{\bb Z}/p}$ , where $V_n$ is the indecomposable ${\bb Z}/p$ -module of dimension $n$ .

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2002

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