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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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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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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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Annihilating Polynomials for Group Rings and Witt Rings
Canadian Mathematical Bulletin, 1989AbstractNatural annihilating polynomials for group rings are produced; this yields, as a special case, the annihilating polynomials for Witt rings that have been discovered only recently.
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Ruthenium-Catalyzed Cycloadditions to Form Five-, Six-, and Seven-Membered Rings
Chemical Reviews, 2021Rosalie S Doerksen +2 more
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