Symmetric bilinear forms and quadratic forms
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This article is published in Journal of Algebra.The article was published on 1972-01-01 and is currently open access. It has received 159 citations till now. The article focuses on the topics: ε-quadratic form & Bilinear form.read more
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4-manifolds and Kirby calculus
TL;DR: In this article, the authors introduce surfaces in 4-manifolds complex surfaces and Kirby calculus, a calculus based on handelbodies and Kirby diagrams, which is used for handel bodies and kirby diagrams.
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The Book of Involutions
TL;DR: A comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups is given in this article, which provides the algebra-theoretic foundations for much of the recent work on linear algebraIC groups over arbitrary fields.
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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations.
Robion Kirby,L. C. Siebenmann +1 more
TL;DR: The first connected account of Kirby's and Siebenmann's basic research in this area is given in this article, followed by three articles by the authors that initially appeared between 1968 and 1970.
Book
The Algebraic and Geometric Theory of Quadratic Forms
TL;DR: The classical theory of symmetric bilinear forms and quadratic forms: Bilinear form Quadratic form forms over rational function fields Function fields of quadrics Bilinverse forms and algebraic extensions $u$-invariants Applications of the Milnor conjecture on the norm residue homomorphism of degree two Algebraic cycles: Homology and cohomology Chow groups Steenrod operations Category of Chow motives Quadratically forms and cyclic cycles as mentioned in this paper.
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New bounds in some transference theorems in the geometry of numbers
TL;DR: In this article, the authors give new bounds in certain inequalities concerning mutually reciprocal lattices in R". To formulate the problem, they have introduced some notation and terminology, and treat IR" as an n-dimensional euclidean space with the norm II II II and metric d.
References
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Structure of Algebras
TL;DR: The structure theorems of Wedderburn Simple algebras Crossed products and exponents Cyclic semi-fields Cyclic algeses and $p$ algebases Representations and Riemann matrices Rational division algesbras Involutions of algesbases Special results as discussed by the authors
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Algebraic K-theory and quadratic forms
TL;DR: In this paper, the authors define a graded ring K, F associated to any rational function field F and construct a homomorphism associated with a discrete valuation on F with residue class field F.
Journal ArticleDOI
On Simply-Connected 4-Manifolds
TL;DR: In this paper, the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds was studied and it was shown that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and induces the tangent bundle of Mx from that of M2.
Book ChapterDOI
Composition algebras and their automorphisms
TL;DR: In this article, the problem of determining the quadratic forms of composition algebras which permit composition has been studied in general and for the case of characteristic not two.
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Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. (Teil I.).
TL;DR: In this paper, Hasse et al. untersuchen in W. Q. den dort nicht betrachteten Fall untersuchhen, daß k die Charakteristik 2 hat.