Mathieu Subspaces of Univariate Polynomial Algebras

Details Mathieu Subspaces of Univariate Polynomial Algebras Mathieu Subspaces of Univariate Polynomial Algebras

2010-12-09

arxiv.org/abs/1012.2017v1

Mathematics

Commutative Algebra

Latex, 22 pages

Scientific paper

We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is true. We also prove two special cases of the one-dimensional Image Conjecture for univariate polynomial algebras $A[t]$ over commutative $\Bbb Q$-algebras $A$.

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