Presentation of rational Schur algebras

We present rational Schur algebra S(n,r,s) over an arbitrary ground field K as a quotient of the distribution algebra Dist(G) of the general linear group G=GL(n) by an ideal I(n,r,s) and provide an explicit description of the generators of I(n,r,s). Over fields K of characteristic zero, this corrects and completes a presentation of S(n,r,s) in terms of generators and relations originally considered by Dipper and Doty. The explicit presentation over ground fields of positive characteristics appears here for the first time.