## Abstract

Let A be a commutative algebra over the field F
_{2}=Z/2. We show that there is a natural algebra homomorphism ℓ(A)→HC
_{⁎}
^{−}(A) which is an isomorphism when A is a smooth algebra. Thus, the functor ℓ can be viewed as an approximation of negative cyclic homology and ordinary cyclic homology HC
_{⁎}(A) is a natural ℓ(A)-module. In general, there is a spectral sequence E
^{2}=L
_{⁎}(ℓ)(A)⇒HC
_{⁎}
^{−}(A). We find associated approximation functors ℓ
^{+} and ℓ
^{per} for ordinary cyclic homology and periodic cyclic homology, and set up their spectral sequences. Finally, we discuss universality of the approximations.

Original language | English |
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Journal | Journal of Pure and Applied Algebra |

Volume | 221 |

Issue | 6 |

Pages (from-to) | 1458–1493 |

Number of pages | 38 |

ISSN | 0022-4049 |

DOIs | |

Publication status | Published - Jun 2017 |