I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2013, VOLUME 18, NUMBER 3, PAGES 69-76
Symmetric polynomials and nonfinitely generated
E. A. da Costa
A. N. Krasilnikov
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a field and let
be the set of all positive integers.
Let be the
ring of polynomials in
be the groups of permutations of the sets
a natural way: and
be the subalgebra of (-)symmetric
polynomials in , i.e.,
is called -invariant if
In 1992, the second author proved that if
then every -invariant ideal
is finitely generated (as such).
In this note, we prove that this is not the case if .
We also survey some results about -invariant ideals in
polynomial algebras and some related topics.
Last modified: March 4, 2014