95-26

The Lasker-Noether Theorem for P*-Invariant Ideals

by Neusel, M. D.; Smith, L.

 

Preprint series: 95-26, Preprints

The paper is published: Forum Math. 10, No.1, 1-18 (1998)

MSC:
55S10 Steenrod algebra
13A50 Invariant theory, See also {14D25}

 

Abstract: This article is motivated by the study begun in L. Smith: P \Lambda -Invariant Ide-als in Rings of Invariants, Form. Math. (to appear), of modular invariantsof finite groups using as tools, the Steenrod algebra and the Dickson alge-bra. The ring of invariants IF[V[] G of a representation ae : G ,! GL(n; IF)of a finite group G over a Galois field IF of characteristic p is an unstablegraded connected commutative Noetherean algebra over the Steenrod alge-bra P \Lambda . We adopt this more general point of view and study P \Lambda -invariantideals in unstable graded connected commutative Noetherean algebras H \Lambdaover a Galois field IF. (An ideal I ae H \Lambda is called P \Lambda -invariant if it isclosed under the action of the Steenrod algebra.) Our goal is to show thatP \Lambda -invariant ideals have a P \Lambda -invariant primary decomposition.Fakultt fr MathematikUniversitt MagdeburgD--39016 Magdeburge--mail: mara.neusel@mathematik.uni-magdeburg.de


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