# algebraic map

A map $f:X\to Y$ between quasi-affine varieties $X\subset {k}^{n},Y\subset {k}^{m}$ over a field $k$ is called if there is a map ${f}^{\prime}:{k}^{n}\to {k}^{m}$ whose component functions are polynomials, such that ${f}^{\prime}$ restricts to $f$ on $X$.

Alternatively, $f$ is algebraic^{} if the pullback map ${f}^{*}:C(Y)\to C(X)$ maps the coordinate ring of $Y$, $k[Y]$, to the coordinate ring of $X$, $k[X]$.

Title | algebraic map |
---|---|

Canonical name | AlgebraicMap |

Date of creation | 2013-03-22 13:53:41 |

Last modified on | 2013-03-22 13:53:41 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 7 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 14A10 |

Synonym | algebraic |