Manis Valuations and Prüfer Extensions I PDF Download
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Author: Manfred Knebusch
Publisher: Springer
ISBN: 3540456252
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
Author: Manfred Knebusch
Publisher: Springer
ISBN: 3540456252
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
Author: Manfred Knebusch
Publisher: Springer
ISBN: 3319032127
Category : Mathematics
Languages : en
Pages : 202
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Book Description
This volume is a sequel to “Manis Valuation and Prüfer Extensions I,” LNM1791. The Prüfer extensions of a commutative ring A are roughly those commutative ring extensions R / A, where commutative algebra is governed by Manis valuations on R with integral values on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prüfer-Manis) valuations. While in Volume I Prüfer extensions in general and individual PM valuations were studied, now the focus is on families of PM valuations. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Gräter’s work in 1980, a far-reaching extension of the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called “Kronecker extensions,” where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimately goes back to the work of Leopold Kronecker.
Author: Hasna Nelfia
Publisher: Bestari
ISBN: 9790639783
Category :
Languages : en
Pages : 50
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Book Description
Kitty, a Mother Cat have four children, they are very sweet and cute. They are named Manis, Belang, Putih, and Olen. While her family is sleeping, Manis is going out of the fence. A puppy is blocking her steps. How does she save herself? What lesson which is given by the mother cat to their children about survival strategy. There are many interesting stories. Let's read the story of cat family.
Author: R. Zachary Manis
Publisher: Oxford University Press
ISBN: 0190929278
Category : Religion
Languages : en
Pages : 432
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Book Description
Why would a perfectly good and loving God consign anyone to eternal suffering in hell? In Sinners in the Presence of a Loving God, R. Zachary Manis examines in detail the various facets of the problem of hell, considers the reasons why the usual responses to the problem are unsatisfying, and suggests how an adequate solution to the problem can be constructed. Historically, there are four standard explanations of the nature and purpose of hell: traditionalism, annihilationism, the choice model, and universalism. In Manis's assessment, all are deficient in some crucial respect. The alternative view that he develops and defends, the divine presence model, stands within the tradition that understands hell to be a state of eternal conscious suffering, but, Manis contends, avoids the worst problems of its competitors. The key idea is that the suffering of hell is not the result of a divine act that aims to inflict it, but rather is the way in which a sinful creature necessarily experiences the unmitigated presence of a holy God. Heaven and hell are not two "places" to which the saved and damned are consigned, respectively, but rather are two radically different ways in which different persons will experience the same reality of God's omnipresence once the barrier of divine hiddenness is finally removed.
Author: William Livingston
Publisher:
ISBN:
Category : American periodicals
Languages : en
Pages : 840
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 1606
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Author: California (State).
Publisher:
ISBN:
Category : Law
Languages : en
Pages : 70
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Court of Appeal Case(s): D008276
Author: Sara Blau
Publisher: It's Good to Know Publishing
ISBN: 9780986277047
Category :
Languages : en
Pages : 30
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Book Description
Teaching Children Their Purpose. A bunch of kids, playing in a tree, Just a few of my friends and little old me! Until Zaidy comes by with something to say, words to remember every day!
Author: Hermann Schlegel
Publisher:
ISBN:
Category :
Languages : en
Pages : 292
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Author:
Publisher:
ISBN:
Category : Ticks
Languages : en
Pages : 350
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