Knebusch, Manfred.
Manis Valuations and Prüfer Extensions I A New Chapter in Commutative Algebra / [electronic resource] : by Manfred Knebusch, Digen Zhang. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2002. - CCLXXXIV, 274 p. online resource. - Lecture Notes in Mathematics, 1791 1617-9692 ; . - Lecture Notes in Mathematics, 1791 .
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.
9783540456254
10.1007/b84018 doi
Mathematics.
Geometry, algebraic.
Algebra.
Mathematics.
Commutative Rings and Algebras.
Algebraic Geometry.
QA251.3
512.44
Manis Valuations and Prüfer Extensions I A New Chapter in Commutative Algebra / [electronic resource] : by Manfred Knebusch, Digen Zhang. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2002. - CCLXXXIV, 274 p. online resource. - Lecture Notes in Mathematics, 1791 1617-9692 ; . - Lecture Notes in Mathematics, 1791 .
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.
9783540456254
10.1007/b84018 doi
Mathematics.
Geometry, algebraic.
Algebra.
Mathematics.
Commutative Rings and Algebras.
Algebraic Geometry.
QA251.3
512.44