Document Zbl 0872.55016 - zbMATH Open
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\(\mathcal{P}^*\)-invariant ideals in rings of invariants. (English) Zbl 0872.55016
If \(F\) is the Galois field with prime number of elements then its Steenrod algebra \({\mathcal P}^*\) acts on the ring of invariants concerning an \(n\)-dimensional representation over \(F\) of a finite group \(G\). The author first explains how to extend the definition of the Steenrod operations to an arbitrary Galois field \(F\). So he gets a similar action on the respective ring of invariants. Then he studies the ideals in the ring that are invariant under the action of \({\mathcal P}^*\). All this has applications to the transfer map from the algebra of polynomial functions on \(F^n\) into the ring of invariants which generalize, for example, an older unpublished result of M. Feshbach [The image of the trace in the ring of invariants. Preprint Univ. Minnesota 1981]. See also [the author, Polynomial invariants of finite groups. Res. Notes Math. 6 (1995; Zbl 0864.13002)].