English

Column symmetric polynomials

Commutative Algebra 2018-12-19 v1

Abstract

We study the polynomial algebra (over a ring containing the rationals) in an n by m matrix of variables, and subject to the relation that says that the product of any two variables in the same column is zero. We show that the sub-algebra of polynomials, which are invariant under n! permutations of the columns, is a quotient of the polynomial algebra in m variables; the quotient map sends the ith variable to the sum of the entries in the ith row of the matrix. - An application in synthetic differential geometry is sketched

Keywords

Cite

@article{arxiv.1812.07021,
  title  = {Column symmetric polynomials},
  author = {Eduardo Dubuc and Anders Kock},
  journal= {arXiv preprint arXiv:1812.07021},
  year   = {2018}
}
R2 v1 2026-06-23T06:45:10.583Z