Jacobi-Zariski long nearly exact sequences for associative algebras

Abstract

For an extension of associative algebras (Formula presented.) over a field and an (Formula presented.) -bimodule (Formula presented.), we obtain a Jacobi–Zariski long nearly exact sequence relating the Hochschild homologies of (Formula presented.) and (Formula presented.), and the relative Hochschild homology, all of them with coefficients in (Formula presented.). This long sequence is exact twice in three. There is a spectral sequence which converges to the gap of exactness.