Dieudonne Determinants for Skew Polynomial Rings TeX Export

@article{citeulike:6058470, abstract = {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.}, archivePrefix = {arXiv}, author = {Taelman, Lenny}, citeulike-article-id = {6058470}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0304478}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0304478}, day = {29}, eprint = {math/0304478}, month = {Apr}, posted-at = {2009-11-03 07:40:06}, priority = {2}, title = {Dieudonne Determinants for Skew Polynomial Rings}, url = {http://arxiv.org/abs/math/0304478}, year = {2003} }

TY - JOUR ID - citeulike:6058470 L3 - citeulike-article-id:6058470 N2 - 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. TI - Dieudonne Determinants for Skew Polynomial Rings AU - Taelman, Lenny PY - 2003/Apr/29/ UR - http://arxiv.org/abs/math/0304478 ER -