The Kiinneth Formula in Cyclic Homology
نویسندگان
چکیده
The cyclic homology H C*(A) of an associative algebra with unit A over a field k of characteristic zero was introduced by A. Connes [C1], and extended to arbitrary commutative rings k in [LQ]. It comes equipped with a natural degree (-2) k-linear map S: HC*(A)~HC*_2(A). We will occasionally write S as SA to indicate dependence on the ring A; the map SA provides HC*(A) with a natural k[u] co-module structure (as described below) via the isomorphism HC*(k)~k[u], deg(u)~2. Throughout, k will be an arbitrary commutative ring with unit. The principal result of this paper is an Eilenberg-Zilber theorem for cyclic k-modules (Theorem 3.1) whose main applications are Theorem A and Theorem B.
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