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The aim of this paper is to show that the topological Hochschild homology of a discrete ring R in the sense of [2] and the MacLane homology of R (see [lo] or [S]) are isomorphic. The method is to show that they are both isomorphic to a certain kind of homology of the category of finitely generated projective Rmodules with coefficients in the bifunctor Horn. That the latter agrees with MacLane homology, was shown in [8]; and that it agrees with topological Hochschild homology, is the main result of this paper. In the (appended) last section we describe a related spectral sequence.

MacLane homology and topological Hochschild homology