A new chapter in commutative algebra
著者
書誌事項
A new chapter in commutative algebra
（Lecture notes in mathematics, 1791 . Manis valuations and prüfer extensions ; 1）
Springer, c2002
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注記
Bibliography: p. [257]-262
Includes indexes
内容説明・目次
内容説明
The present book is devoted to a study of relative Prufer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.
目次
Introduction.- Basics on Manis valuations and Prufer extensions.- Multiplicative ideal theory.- PM-valuations and valuations of weaker type.- Appendix A: Flat epimorphisms.- Appendix B: Arithmetical rings.- Appendix C: A direct proof of the existence of Manis valuation hulls.- References.- Index.
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