Annihilating polynomials for quadratic forms

Lewis, David W.

doi:10.1155/s0161171201011279

Cited by 5 publications

(6 citation statements)

References 10 publications

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“…The additive group [1][2][3] of the residue class ring [4][5] mod m is, up to isomorphism, the cyclic group of order m generate, say, by the residue class 1 mod m. For finite group, the direct sum decomposition [6] with respect to the prime power appearing in m is simply a special case of the basis theorem for finite abelian groups, according to the sum of cyclic subgroups of prime power order. Here, however, the direct sum of each cyclic subgroup belongs to the same prime number, rather than the direct sums of the cyclic subgroups themselves, which are uniquely determined.…”

Section: Introductionmentioning

confidence: 99%

Discussion on the Structure of the Reduced Residue Class Additive Group in Cyclic Group

Zeng¹

2020

dtssehs

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Additive group in the group theory is an important tool to research group. Studying of different kinds of additive group is helpful to the study group. The method itself can be applied to esearch the other in the natural sciences. In this paper, a class of additive group of the residue class ring mod m has been studied. The properties of the residue class ring and the formula for Euler 's function were used. Finally, the order of group and its prime factor of the corresponding cyclic group were used to depict the structure of this kind of group.

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Section: Introductionmentioning

confidence: 99%

Discussion on the Structure of the Reduced Residue Class Additive Group in Cyclic Group

Zeng¹

2020

dtssehs

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“…Some effort has also been put into determining the ideal consisting of those polynomials which annihilate the whole Witt ring, its fundamental ideal, or its torsion subgroup ( [OG97] and [Wan07]). A survey of many of the currently known results about annihilating polynomials of quadratic forms can be found in [Lew01].…”

Section: Introductionmentioning

confidence: 99%

Annihilating Ideals of Quadratic Forms Over Local and Global Fields

Rühl

2010

Int. J. Number Theory

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We study annihilating polynomials and annihilating ideals for elements of Witt rings for groups of exponent 2. With the help of these results and certain calculations involving the Clifford invariant we are able to give full sets of generators for the annihilating ideal of both the isometry class and the equivalence class of an arbitrary quadratic form over a local field. By applying the Hasse-Minkowski theorem we can then achieve the same for an arbitrary quadratic form over a global field.

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“…positive forms and trace forms. An extensive survey of the currently known results about annihilating polynomials of quadratic forms can be found in [6].…”

Section: Introductionmentioning

confidence: 99%