Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 353368 (2004) 

When is the algebra of multisymmetric polynomials generated by the elementary multisymmetric polynomials?Emmanuel BriandAbstract: Multisymmetric polynomials are the $r$fold diagonal invariants of the symmetric group ${\mathfrak{S}}_n$. Elementary multisymmetric polynomials are analogues of the elementary symmetric polynomials, in the multisymmetric setting. In this paper, we give a necessary and sufficient condition on a ring $A$ for the algebra of multisymmetric polynomials with coefficients in $A$ to be generated by the elementary multisymmetric polynomials. Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
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