  Quadratic algebras associated to pseudo-roots of noncommutative polynomials
have been introduced by I. Gelfand, Retakh, and Wilson in connection with
studying the decompositions of noncommutative polynomials. Later they (with S.
Gelfand and Serconek) shown that the Hilbert series of these algebras and their
quadratic duals satisfy the necessary condition for Koszulity. It is proved in
this note that these algebras are Koszul.
