  Motivated by work of R.M. Green, we obtain a presentation of Schur algebras
(both the classical and quantized versions) in terms of generators and
relations. The presentation is compatible with the usual presentation of the
(quantized or classical) enveloping algebra of gl(n). As a result, we obtain a
new ``integral'' basis for Schur algebras which is a subset of Kostant's basis
of the integral form of the enveloping algebra (or its q-analogue). Projection
onto an appropriate component gives a new "integral" basis and a presentation
for the Hecke algebra, compatible with the basis and presentation for the Schur
algebra. Finally, we find a second presentation of Schur algebras which is
similar to Luzstig's modified form of the quantized enveloping algebra.
