NOETHER NUMBERS FOR SUBREPRESENTATIONS OF CYCLIC GROUPS OF PRIME ORDER
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Let W be a finite-dimensional �/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W] �/p, is called the Noether number of the representation, and is denoted by β(W). A lower bound for β(W) is derived, and it is shown that if U is a �/p submodule of W, then β(U) � β(W). A set of generators, in fact a SAGBI basis, is constructed for k[V2 ⊕ V3] �/p, where Vn is the indecomposable �/p-module of dimension n. 1.