Let k be a field and I an H-unital two-sided ideal of an associative unital k-algebra A. Then, based on Wodzicki's work, we show that the Hochschild homology groups of A with coefficients in I are isomorphic to the Hochschild homology groups of I.
Homology, Homotopy and Applications, Vol. 11 (2009), No. 2, pp.1-4.