We introduce the notion of non commutative truncated polynomial extension of an algebra . A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper triangular, we find that the obstructions to inductively construct them, lie in the Hochschild homology of . A, with coefficients in a suitable . A-bimodule. © 2012 Elsevier B.V.