Zobrazeno 1 - 10
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pro vyhledávání: '"Zemková, Kristýna"'
Autor:
Lorenz, Nico, Zemková, Kristýna
Publikováno v:
J. Pure Appl. Algebra 228(12) (2024)
Let $F$ be a field of characteristic $2$, $\pi$ be an $n$-fold bilinear Pfister form over $F$ and $\varphi$ an arbitrary quadratic form over $F$. In this note, we investigate Witt index, defect, total isotropy index and higher isotropy indices of $\v
Externí odkaz:
http://arxiv.org/abs/2401.12515
Autor:
Zemková, Kristýna
Publikováno v:
Pacific J. Math. 329 (2024) 327-356
For quadratic forms over fields of characteristic different from two, there is a so-called Vishik criterion, giving a purely algebraic characterization of when two quadratic forms are motivically equivalent. In analogy to that, we define Vishik equiv
Externí odkaz:
http://arxiv.org/abs/2309.13346
Autor:
Zemková, Kristýna
Publikováno v:
J. Algebra 657 (2024)
For a quasilinear $p$-form defined over a field $F$ of characteristic $p>0$, we prove that its defect over the field $F(\sqrt[p^{n_1}]{a_1}, \dots, \sqrt[p^{n_r}]{a_r})$ equals to its defect over the field $F(\sqrt[p]{a_1}, \dots, \sqrt[p]{a_r})$, st
Externí odkaz:
http://arxiv.org/abs/2309.13341
Autor:
Zemková, Kristýna
Publikováno v:
Comm. Algebra 52(10) (2024)
We extend to characteristic two recent results about isotropy of quadratic forms over function fields. In particular, we provide a characterization of function fields not only of quadratic forms but also more generally of polynomials in several varia
Externí odkaz:
http://arxiv.org/abs/2206.05987
Autor:
Zemková, Kristýna
The thesis is concerned with the theory of binary quadratic forms with coefficients in the ring of algebraic integers of a number field. Under the assumption that the number field is of narrow class number one, there is developed a theory of composit
Externí odkaz:
http://www.nusl.cz/ntk/nusl-383320
Autor:
Zemková, Kristýna
In this paper, the composition of Bhargava's cubes is generalized to the ring of integers of a number field of narrow class number one, excluding the case of totally imaginary number fields.
Comment: 21 pages; an appendix on totally imaginary nu
Comment: 21 pages; an appendix on totally imaginary nu
Externí odkaz:
http://arxiv.org/abs/1911.00431
Publikováno v:
Proceedings of the Edinburgh Mathematical Society 63 (2020) 861-912
We study totally positive definite quadratic forms over the ring of integers $\mathcal{O}_K$ of a totally real biquadratic field $K=\mathbb{Q}(\sqrt{m}, \sqrt{s})$. We restrict our attention to classical forms (i.e., those with all non-diagonal coeff
Externí odkaz:
http://arxiv.org/abs/1909.05422
The aim of this article is to study (additively) indecomposable algebraic integers $\mathcal O_K$ of biquadratic number fields $K$ and universal totally positive quadratic forms with coefficients in $\mathcal O_K$. There are given sufficient conditio
Externí odkaz:
http://arxiv.org/abs/1802.07811
Autor:
Zemková, Kristýna
Publikováno v:
Math. Slovaca, 71(6), 2021
In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one. The
Externí odkaz:
http://arxiv.org/abs/1712.00741