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of 286
pro vyhledávání: '"Chapman, Adam"'
Let $F$ be a field of characteristic $p>0$. We prove that if a symbol $A=\omega \otimes \beta_1 \otimes \dots \otimes \beta_n$ in $H_{p^m}^{n+1}(F)$ is of exponent dividing $p^{m-1}$, then its symbol length in $H_{p^{m-1}}^{n+1}(F)$ is at most $p^n$.
Externí odkaz:
http://arxiv.org/abs/2409.16447
Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra H. We describe the "algebraic hull" of a point in H^n and prove it is
Externí odkaz:
http://arxiv.org/abs/2408.08246
We study mixed multiquadratic field extensions as splitting fields for central simple algebras of exponent $2$ in characteristic $2$. As an application, we provide examples of nonexcellent mixed biquadratic field extensions.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2406.14339
Autor:
Chapman, Adam, Levin, Ilan
We associate an $(n_1+\dots+n_t-k(t-1))$-fold Pfister form to any $t$-tuple of $k$-linked Pfister forms of dimensions $2^{n_1},\dots,2^{n_t}$, and prove its invariance under the different symbol presentations of the forms with a common $k$-fold sub-s
Externí odkaz:
http://arxiv.org/abs/2404.00121
Autor:
Chapman, Adam
We prove that the maximal dimension of a subspace $V$ of the generic tensor product of $m$ symbol algebras of prime degree $p$ with $\operatorname{Tr}(v^{p-1})=0$ for all $v\in V$ is $\frac{p^{2m}-1}{p-1}$. The same upper bound is thus obtained for $
Externí odkaz:
http://arxiv.org/abs/2403.13080
Autor:
Chapman, Adam
We prove that two cyclically linked $p$-algebras of prime degree become inseparably linked under a prime to $p$ extension if and only if the essential $p$-dimension of the pair is 2. We conclude that the essential $p$-dimension of pairs of cyclically
Externí odkaz:
http://arxiv.org/abs/2403.11154
Autor:
Chapman, Adam, Srimathy, S.
We conjecture that a $p$-algebra over a complete discrete valued field $K$ contains a totally ramified purely inseparable subfield if and only if it contains a totally ramified cyclic maximal subfield. We prove the conjecture in several cases.
Externí odkaz:
http://arxiv.org/abs/2402.10829
Roots and right factors of polynomials and left eigenvalues of matrices over Cayley-Dickson algebras
Autor:
Chapman, Adam, Vishkautsan, Solomon
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar) (February 27, 2024) cm:12613
Over a composition algebra $A$, a polynomial $f(x) \in A[x]$ has a root $\alpha$ if and only $f(x)=g(x)\cdot (x-\alpha)$ for some $g(x) \in A[x]$. We examine whether this is true for general Cayley-Dickson algebras. The conclusion is that it is when
Externí odkaz:
http://arxiv.org/abs/2311.16704
Autor:
Chapman, Adam, Levin, Ilan
Publikováno v:
Communications in Mathematics, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") (October 26, 2023) cm:11514
We introduce the notions of alternating roots of polynomials and alternating polynomials over a Cayley-Dickson algebra, and prove a connection between the alternating roots of a given polynomial and the roots of the corresponding alternating polynomi
Externí odkaz:
http://arxiv.org/abs/2306.15889
Autor:
Chapman, Adam, McKinnie, Kelly
In this note, we present a chain lemma for biquaternion algebras over fields of characteristic 2 in the style of the equivalent chain lemma by Sivatski in characteristic not 2, and conclude a bound on the symbol length of classes in ${_{2^n}Br}(F)$ w
Externí odkaz:
http://arxiv.org/abs/2306.08525