WorldCat Identities

Knebusch, Manfred

Overview
Works: 41 works in 199 publications in 2 languages and 3,193 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Creator
Classifications: QA3, 512.942
Publication Timeline
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Most widely held works by Manfred Knebusch
Locally semialgebraic spaces by Hans Delfs( Book )

17 editions published in 1985 in 3 languages and held by 349 WorldCat member libraries worldwide

Weakly semialgebraic spaces by Manfred Knebusch( Book )

17 editions published in 1989 in English and Undetermined and held by 337 WorldCat member libraries worldwide

The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA(R) or regular paracompact locally semialgebraic spaces over R was studied. The category WSA(R) of weakly semialgebraic spaces over R - the focus of this new volume - contains LSA(R) as a full subcategory. The book provides ample evidence that WSA(R) is "the" right cadre to understand homotopy and homology of semialgebraic sets, while LSA(R) seems to be more natural and beautiful from a geometric angle. The semialgebraic sets appear in LSA(R) and WSA(R) as the full subcategory SA(R) of affine semialgebraic spaces. The theory is new although it borrows from algebraic topology. A highlight is the proof that every generalized topological (co)homology theory has a counterpart in WSA(R) with in some sense "the same", or even better, properties as the topological theory. Thus we may speak of ordinary (=singular) homology groups, orthogonal, unitary or symplectic K-groups, and various sorts of cobordism groups of a semialgebraic set over R. If R is not archimedean then it seems difficult to develop a satisfactory theory of these groups within the category of semialgebraic sets over R: with weakly semialgebraic spaces this becomes easy. It remains for us to interpret the elements of these groups in geometric terms: this is done here for ordinary (co)homology
Manis valuations and Prüfer extensions I : a new chapter in commutative algebra by Manfred Knebusch( Book )

29 editions published between 2002 and 2004 in English and held by 304 WorldCat member libraries worldwide

The present book is devoted to a study of relative Prfer 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
Algebraic theory of quadratic forms : generic methods and Pfister forms by Manfred Knebusch( Book )

14 editions published in 1980 in English and Undetermined and held by 269 WorldCat member libraries worldwide

Wittrings by Manfred Knebusch( Book )

13 editions published between 1972 and 1982 in 3 languages and held by 210 WorldCat member libraries worldwide

Manis valuations and Prüfer extensions II by Manfred Knebusch( Book )

17 editions published in 2014 in English and held by 109 WorldCat member libraries worldwide

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
Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen by Manfred Knebusch( Book )

10 editions published in 1970 in German and English and held by 84 WorldCat member libraries worldwide

Einführung in die reelle Algebra by Manfred Knebusch( Book )

11 editions published between 1989 and 2002 in German and held by 75 WorldCat member libraries worldwide

Specialization of quadratic and symmetric bilinear forms by Manfred Knebusch( Book )

15 editions published between 2010 and 2013 in English and held by 71 WorldCat member libraries worldwide

The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t
Ordnungen in lokalen Jordanalgebren vom Grade 2 und 3 by Manfred Knebusch( )

7 editions published in 1964 in German and held by 33 WorldCat member libraries worldwide

Supertropical Linear Algebra by Zur Izhakian( Book )

2 editions published in 2010 in German and English and held by 18 WorldCat member libraries worldwide

Supertropical Semirings and Supervaluations by Zur Ishakian( )

1 edition published in 2010 in German and held by 15 WorldCat member libraries worldwide

Conference on Quadratic Forms, 1976 by T. Y Lam( Book )

1 edition published in 1977 in English and held by 14 WorldCat member libraries worldwide

Wittringe by Manfred Knebusch( Book )

4 editions published between 1972 and 1978 in German and English and held by 9 WorldCat member libraries worldwide

Wittringe : Nach e. Vorlesung 1971-72 in Saarbrücken by Manfred Knebusch( Book )

1 edition published in 1978 in German and held by 5 WorldCat member libraries worldwide

Generic splitting towers and generic splitting preparation of quadratic forms by Manfred Knebusch( Book )

3 editions published in 2000 in English and held by 5 WorldCat member libraries worldwide

Manis valuations and Prüfer extensions by Manfred Knebusch( Book )

in Undetermined and English and held by 5 WorldCat member libraries worldwide

Dominance and transmissions in supertropical valuation theory by Zur Izhakian( Book )

2 editions published in 2011 in English and held by 3 WorldCat member libraries worldwide

Monoid valuations and value ordered supervaluations by Zur Izhakian( Book )

2 editions published in 2011 in German and English and held by 3 WorldCat member libraries worldwide

Supertropical quadratic forms by Zur Izhakian( Book )

3 editions published in 2013 in English and German and held by 1 WorldCat member library worldwide

 
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Audience level: 0.71 (from 0.50 for Specializa ... to 0.94 for Generic sp ...)

Weakly semialgebraic spaces
Alternative Names
Knebusch, Manfred

Manfred Knebusch deutscher Mathematiker

Manfred Knebusch Duits wiskundige

Manfred Knebusch German mathematician

Manfred Knebusch tysk matematikar

Manfred Knebusch tysk matematiker

Languages
English (129)

German (38)

Covers
Weakly semialgebraic spacesManis valuations and Prüfer extensions I : a new chapter in commutative algebraSpecialization of quadratic and symmetric bilinear formsManis valuations and Prüfer extensions