Dieudonne Determinants for Skew Polynomial Rings

Details Dieudonne Determinants for Skew Polynomial Rings Dieudonne Determinants for Skew Polynomial Rings

2003-04-29

arxiv.org/abs/math/0304478v1

Mathematics

Rings and Algebras

4 pages

Scientific paper

We observe that the Dieudonn\'{e} determinant induces a non-negative degree function on the ring of matrices over a skew polynomial ring. We then apply this degree function to two examples. In the first one, we find an expression for the rank of the kernel of an endomorphism of the algebraic group $\mathbb{G}_a^n$ over a field of characteristic $p>0$. In the second, we calculate the dimension of the solution space of linear matrix differential equations.

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