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Comprehensive review of understanding ancient dietary habits using modern analytical techniques. [PDF]
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The Annals of Mathematics, 1996
This paper is concerned with the connections between the Witt ring of a field and the structure of certain Galois extensions of that field. In particular, it is shown that the Witt ring determines, and is determined by, the Galois group of a certain 2-extension of the field (with an unavoidable uncertainty over the characteristic of the Witt ring in ...
Mináč, Ján, Spira, Michel
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This paper is concerned with the connections between the Witt ring of a field and the structure of certain Galois extensions of that field. In particular, it is shown that the Witt ring determines, and is determined by, the Galois group of a certain 2-extension of the field (with an unavoidable uncertainty over the characteristic of the Witt ring in ...
Mináč, Ján, Spira, Michel
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Canadian Journal of Mathematics, 1982
We take the definition of a Witt ring to be that given in [13], i.e., it is what is called a strongly representational Witt ring in [8]. The classical example is obtained by considering quadratic forms over a field of characteristic ≠ 2 [17], but Witt rings also arise in studying quadratic forms or symmetric bilinear forms over more general types of ...
Carson, Andrew B., Marshall, Murray A.
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We take the definition of a Witt ring to be that given in [13], i.e., it is what is called a strongly representational Witt ring in [8]. The classical example is obtained by considering quadratic forms over a field of characteristic ≠ 2 [17], but Witt rings also arise in studying quadratic forms or symmetric bilinear forms over more general types of ...
Carson, Andrew B., Marshall, Murray A.
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Polynomials Annihilating the Witt Ring
Mathematische Nachrichten, 1997AbstractLet F be a non‐formally real field of characteristic not 2 and let W(F) be the Witt ring of F. In certain cases generators for the annihilator ideal equation image are determined. Aim the primary decomposition of A(F) is given. For formally d fields F, as an analogue the primary decomposition of At(F) = {f(X) ∈ Z[X]| f(ω) = 0 for all ω ∈ Wt(F)
Ongenae, Veerle, van Geel, Jan
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Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings
Canadian Journal of Mathematics, 1978This paper originated in an attempt to carry over the results of [3] from the case of a field of characteristic different from two to that of semilocal rings. To carry this out, we reverse the point of view of [3] and do assume a full knowledge of the theory of Witt rings of classes of nondegenerate symmetric bilinear forms over semilocal rings as ...
Kleinstein, Jerrold L., Rosenberg, Alex
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Mathematics of the USSR-Izvestiya, 1968
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Canadian Journal of Mathematics, 1988
Throughout R is a noetherian Witt ring. The basic example is the Witt ring WF of a field F of characteristic not 2 and finite. We study the structure of (noetherian) Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). The underlying motivation is the elementary type conjecture. The Gorenstein Witt rings of elementary
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Throughout R is a noetherian Witt ring. The basic example is the Witt ring WF of a field F of characteristic not 2 and finite. We study the structure of (noetherian) Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). The underlying motivation is the elementary type conjecture. The Gorenstein Witt rings of elementary
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American Journal of Mathematics, 1991
Let \(F\subset K\) be a field extension. The authors prove a variety of results on Witt rings and Galois cohomology of the ``going-down'' type, i.e. how the behaviour of \(K\) influences that of \(F\). As usual, \(H^ n(F,-)\) denotes the cohomology of the Galois group of a separable algebraic closure of \(F\) and \(F_ q\) the quadratic closure.
Arason, Jón Kr., Elman, Richard
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Let \(F\subset K\) be a field extension. The authors prove a variety of results on Witt rings and Galois cohomology of the ``going-down'' type, i.e. how the behaviour of \(K\) influences that of \(F\). As usual, \(H^ n(F,-)\) denotes the cohomology of the Galois group of a separable algebraic closure of \(F\) and \(F_ q\) the quadratic closure.
Arason, Jón Kr., Elman, Richard
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Witt Rings and Permutation Polynomials
Algebra Colloquium, 2005Let p be a prime number. In this paper, the author sets up a canonical correspondence between polynomial functions over ℤ/p2ℤ and 3-tuples of polynomial functions over ℤ/pℤ. Based on this correspondence, he proves and reproves some fundamental results on permutation polynomials mod pl.
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Isomorphisms and Automorphisms of Witt Rings
Canadian Mathematical Bulletin, 1988AbstractFor a field F, char(F) ≠ 2, let WF denote the Witt ring of quadratic forms of F and let denote the multiplicative group of 1-dimensional forms It follows from a construction of D. K. Harrison that if E, F are fields (both of characteristic ≠ 2) and ρ.WE → WF is a ring isomorphism, then there exists a ring isomorphism which “preserves ...
Leep, David, Marshall, Murray
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