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Catalogue Information
Field name	Details
Dewey Class	512.44
Title	Manis Valuations and Prüfer Extensions I ([EBook] :) : A New Chapter in Commutative Algebra / / by Manfred Knebusch, Digen Zhang.
Author	Knebusch, Manfred
Added Personal Name	Zhang, Digen author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 2002.
Physical Details	CCLXXXIV, 274 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1791
ISBN	9783540456254
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b84018
Links to Related Works	Subject References: Algebraic Geometry . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Mathematics . Authors: Knebusch, Manfred . Zhang, Digen . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.44 .

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Manis Valuations and Prüfer Extensions I: A New Chapter in Commutative Algebra /

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