We prove that for an inclusion of unital associative but not necessarily commutative k-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 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.
Homology, Homotopy and Applications, Vol. 14 (2012), No. 1, pp.65-78.
doi:10.4310/HHA.2012.v14.n1.a4
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