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The Lasker-Noether Theorem for P*-Invariant Ideals

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

Series: 1995-26, Preprints

55S10 Steenrod algebra
13A50 Actions of groups on commutative rings; invariant theory

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 invariants
of 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 unstable
graded connected commutative Noetherean algebra over the Steenrod alge-
bra P \Lambda . We adopt this more general point of view and study P \Lambda -invariant
ideals in unstable graded connected commutative Noetherean algebras H \Lambda
over a Galois field IF. (An ideal I ae H \Lambda is called P \Lambda -invariant if it is
closed under the action of the Steenrod algebra.) Our goal is to show that
P \Lambda -invariant ideals have a P \Lambda -invariant primary decomposition.
Fakultät für Mathematik
Universität Magdeburg
D--39016 Magdeburg
e--mail: mara.neusel@mathematik.uni-magdeburg.de


This paper was published in:
Forum Math. 10, No.1, 1-18 (1998)