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In this survey paper we study the relationships between the coarse modulispace which parameterizes the finite dimensional linear representations of anassociative alegebra, the non commutative hilbert scheme and the affine schemewhich is the spectrum of the abelianization of algebra of the divided powers.In particular we will show a map which specialize to the Hlibert - Chowmorphism when the associative algebra is commutative. The extension to thepositive characteristic case of some of the results due to L. Le Bruyn onnoncommutative desingularization is outlined. The possibility to use ourconstruction to extend the work done by C.H.Liu and S.T.Yau on D-Branes totheir more recent work on non commutative case is underlined.

Moduli of linear representations, symmetric products and the non commutative Hilbert scheme