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Record Nr. |
UNISA996466608303316 |
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Autore |
Knebusch Manfred |
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Titolo |
Manis Valuations and Prüfer Extensions I [[electronic resource] ] : A New Chapter in Commutative Algebra / / by Manfred Knebusch, Digen Zhang |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 |
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ISBN |
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Edizione |
[1st ed. 2002.] |
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Descrizione fisica |
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1 online resource (CCLXXXIV, 274 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1791 |
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Disciplina |
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Soggetti |
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Commutative algebra |
Commutative rings |
Algebraic geometry |
Commutative Rings and Algebras |
Algebraic Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Introduction -- Basics on Manis valuations and Prüfer 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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Sommario/riassunto |
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The present book is devoted to a study of relative Prüfer 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. |
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