Results 161 to 170 of about 73,169 (194)
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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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Canadian Journal of Mathematics, 1997
AbstractThe abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classify the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.
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AbstractThe abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classify the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.
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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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Catalytic Enantioselective Ring-Opening Reactions of Cyclopropanes
Chemical Reviews, 2021Vincent Pirenne +2 more
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