Spectral sequence for MacLane homology
\textit{S. MacLane} has defined the cohomology of a ring \(R\) with coefficients in an \(R\)-\(R\)-bimodule \(M\) based on the Hochschild cohomology of a chain algebra which has the same homology as the Eilenberg-MacLane spectrum [Colloq. Topologie algébrique, Louvain, 1956, 55-80 (1957; Zbl 0084.267)]. Dually one has the MacLane homology. This one and the Hochschild homology are related by a spectral sequence [see the author and \textit{F. Waldhausen}, J. Pure Appl. Algebra 82, No. 1, 81-98 (1992; Zbl 0767.55010)]. In the present paper it is proved that if \(R\) is a monoid ring or a smooth algebra, then the differentials of the spectral sequence are zero. That is also true for algebras over \(\mathbb{F}_ p\) where \(p\) is a prime.
scientific article; zbMATH DE number 703227