## Abstract

This monograph is a comprehensive exposition of the modern theory of valued and ordered fields. It presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. Deeper cohomological aspects are studied in its last part in an elementary manner. This is done by means of the newly developed theory of generalized Milnor K-rings. The book emphasizes the close connections and interplay between valuations and orderings, and to a large extent, studies them in a unified manner.

The presentation is almost entirely self-contained. In particular, the text develops the needed machinery of ordered abelian groups. This is then used throughout the text to replace the more classical techniques of commutative algebra. Likewise, the book provides an introduction to the Milnor K-theory.

The presentation is almost entirely self-contained. In particular, the text develops the needed machinery of ordered abelian groups. This is then used throughout the text to replace the more classical techniques of commutative algebra. Likewise, the book provides an introduction to the Milnor K-theory.

Original language | English |
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Publisher | American Mathematical Society |

Number of pages | 288 |

ISBN (Electronic) | 9781470413514 |

ISBN (Print) | 9780821840412 |

DOIs | |

State | Published - 2006 |

### Publication series

Name | Mathematical surveys and monographs |
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Publisher | American Mathematical Society |

Volume | no. 124 |

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