### 1995-26

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

**Series:** 1995-26, Preprints

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

**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 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

**Keywords:**

**This paper was published in:**

Forum Math. 10, No.1, 1-18 (1998)