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Rings, Polynomials, and Modules
A presentation by generators and relations of the nth symmetric power B of a commutative algebra A over a field of characteristic zero or greater than n is given. This is applied to get information on a minimal homogeneous generating system of B (in the graded case). The known result that in characteristic zero the algebra B is isomorphic to the coordinate ring of the scheme of n-dimensional representations of A is also recovered. The special case when A is the two-variable polynomial algebradoi:10.1007/978-3-319-65874-2_9 fatcat:4qj33ntstfdq5jcfgn4jk3b6uy