The Lasker-Noether theorem for P* - variant ideals

Summary This article is motivated by the study begun in 8 of modular invariants of finite groups using as tools, the Steenrod algebra and the Dickson algebra. The ring of invariants of a representation q : G GL(h, F) of a finite group G over a Galois field F of characteristic p is an unstable graded connected commutative Noetherian algebra over the Steenrod algebra P*. We adopt this more general point of view and study P*-invariant ideals in unstable graded connected commutative Noetherian algebras H* over a Galois field F. (An ideal I= H* is called ,P*-invariant if it is closed under the action of the Steenrod algebra.) Our goal is to show that .P*-invarlant ideals have a .P*-invariant primary decomposition.