A new degree bound for vector invariants
of symmetric groups
Author:
P. Fleischmann
Journal:
Trans. Amer. Math. Soc. 350 (1998), 1703-1712
MSC (1991):
Primary 13A50
DOI:
https://doi.org/10.1090/S0002-9947-98-02064-9
MathSciNet review:
1451600
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a commutative ring,
a finitely generated free
-module and
a finite group acting naturally on the graded symmetric algebra
. Let
denote the minimal number
, such that the ring
of invariants can be generated by finitely many elements of degree at most
.
For and
, the
-fold direct sum of the natural permutation module, one knows that
, provided that
is invertible in
. This was used by E. Noether to prove
if
.
In this paper we prove for arbitrary commutative rings
and show equality for
a prime power and
or any ring with
. Our results imply
for any ring with .
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Additional Information
P. Fleischmann
Affiliation:
Institute for Experimental Mathematics, University of Essen, Ellernstr. 29, 45326 Essen, Germany
Email:
peter@exp-math.uni-essen.de
DOI:
https://doi.org/10.1090/S0002-9947-98-02064-9
Received by editor(s):
June 20, 1996
Article copyright:
© Copyright 1998
American Mathematical Society