## Abstract

We consider the transformation ev which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both ev and its dual ev* are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. This question arises in the classical problem of the reconstruction of a function by its values at a given set of points. The answer is nontrivial for various choices of K and A already for A=K[x], the polynomial ring in one variable. Applications to the structure of algebras of cohomology operations are given.

Translated title of the contribution | The Gelfand transform in commutative algebra |
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Original language | English |

Pages (from-to) | 7 - 23 |

Number of pages | 17 |

Journal | Moscow Mathematical Journal |

Volume | 5 (2) |

Publication status | Published - Apr 2005 |