## Abstract

Any finite degree field extension K/F determines an ideal ^{I}k/f of the Witt ring WF of F, called the transfer ideal, which is the image of any nonzero transfer map WK → WF. The ideal ^{I}k/f is computed for certain field extensions, concentrating on the case where K has the form F(√ a_{1};,&, √ a_{n}), a_{i}ε F. When F and K are global fields, we investigate whether there is a local global principle for membership in ^{I}k/f. This is shown to be equivalent to the existence of a "Hasse norm theorem mod squares, " i.e., a local global principle for the image of the norm map N_{K/F}: KK^{2}→ F/F2. It is shown that such a Hasse norm theorem holds whenever K = F(√ a_{1};,&, √ a_{n}), although it does not always hold for more general extensions of global fields, even some Galois extensions with group Z/2Z × Z/4Z.

Original language | English |
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Pages (from-to) | 415-431 |

Number of pages | 17 |

Journal | Transactions of the American Mathematical Society |

Volume | 315 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1989 |

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics