Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

A note on the kernels of higher derivations

Jiantao LiXiankun Du — 2013

Czechoslovak Mathematical Journal

Let k k ' be a field extension. We give relations between the kernels of higher derivations on k [ X ] and k ' [ X ] , where k [ X ] : = k [ x 1 , , x n ] denotes the polynomial ring in n variables over the field k . More precisely, let D = { D n } n = 0 a higher k -derivation on k [ X ] and D ' = { D n ' } n = 0 a higher k ' -derivation on k ' [ X ] such that D m ' ( x i ) = D m ( x i ) for all m 0 and i = 1 , 2 , , n . Then (1) k [ X ] D = k if and only if k ' [ X ] D ' = k ' ; (2) k [ X ] D is a finitely generated k -algebra if and only if k ' [ X ] D ' is a finitely generated k ' -algebra. Furthermore, we also show that the kernel k [ X ] D of a higher derivation D of k [ X ] can be generated by a set...

Page 1

Download Results (CSV)