International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 4, Pages 201-214

Multivariable dimension polynomials and new invariants of differential field extensions

Alexander B. Levin

Department of Mathematics, The Catholic University of America, Washington 20064, DC, USA

Received 16 February 2001

Copyright © 2001 Alexander B. Levin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin's theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension.