Jacobi-Zariski exact sequence for hochschild homology and cyclic (co)homology

We prove that for an inclusion of unital associative but not necessarily commutative k{double-struck}-algebras B ⊆ A we have long exact sequences in Hochschild homology and cyclic (co)homology akin to the Jacobi-Zariski sequence in André-Quillen homology, provided that the quotient B-module A/B is flat. We also prove that for an arbitrary r-flat morphism φ. B → A with an H-unital kernel, one can express the Wodzicki excision sequence and our Jacobi-Zariski sequence in Hochschild homology and cyclic (co)homology as a single long exact sequence.