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＜電子ブック＞
Manis Valuations and Prüfer Extensions I : A New Chapter in Commutative Algebra / by Manfred Knebusch, Digen Zhang
(Lecture Notes in Mathematics. ISSN:16179692 ; 1791)

版	1st ed. 2002.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2002
大きさ	CCLXXXIV, 274 p : online resource
著者標目	*Knebusch, Manfred author Zhang, Digen author SpringerLink (Online service)
件　名	LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic geometry FREE:Commutative Rings and Algebras FREE:Algebraic Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b84018

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