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|a 9783540456254
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|a 10.1007/b84018
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|a Knebusch, Manfred.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Manis Valuations and Prüfer Extensions I
|h [electronic resource] :
|b A New Chapter in Commutative Algebra /
|c by Manfred Knebusch, Digen Zhang.
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| 250 |
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|a 1st ed. 2002.
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| 264 |
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1 |
|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2002.
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| 300 |
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|a CCLXXXIV, 274 p.
|b online resource.
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| 490 |
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1791
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| 490 |
1 |
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|a Springer eBook Collection
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| 505 |
0 |
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|a 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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| 520 |
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|a 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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| 590 |
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|a Loaded electronically.
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| 590 |
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|a Electronic access restricted to members of the Holy Cross Community.
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| 650 |
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|a Commutative algebra.
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| 650 |
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|a Commutative rings.
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| 650 |
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|a Algebraic geometry.
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| 690 |
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|a Electronic resources (E-books)
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| 700 |
1 |
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|a Zhang, Digen.
|e author.
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