Jacobi–Zariski long nearly exact sequences for associative algebras.

For an extension of associative algebras B⊂A over a field and an A‐bimodule X, we obtain a Jacobi–Zariski long nearly exact sequence relating the Hochschild homologies of A and B, and the relative Hochschild homology, all of them with coefficients in X. This long sequence is exact twice in three. There is a spectral sequence which converges to the gap of exactness. [ABSTRACT FROM AUTHOR]