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

• Main Authors: Knebusch, Manfred (Author, http://id.loc.gov/vocabulary/relators/aut), Zhang, Digen (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1791
• Subjects: Commutative algebra.; Commutative rings.; Algebraic geometry.; Commutative Rings and Algebras.; Algebraic Geometry.
• Physical Description: CCLXXXIV, 274 p. online resource.
• ISBN: 9783540456254
• ISSN: 0075-8434 ;
• DOI: 10.1007/b84018

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.