Zobrazeno 1 - 10
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pro vyhledávání: '"Brešar, Matej"'
Autor:
Brešar, Matej
We define a Jordan homomorphism $\varphi$ from a ring $R$ to a ring $R'$ to be splittable if the ideal (of the subring generated by the image of $\varphi$) generated by all $\varphi(xy)-\varphi(x)\varphi(y)$, $x,y\in R$, has trivial intersection with
Externí odkaz:
http://arxiv.org/abs/2410.07052
Autor:
Brešar, Matej
The celebrated Wedderburn-Artin theorem states that a simple left artinian ring is isomorphic to the ring of matrices over a division ring. We give a short and self-contained proof which avoids the use of modules.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2405.04588
Autor:
Brešar, Matej
Frobenius' Theorem states that the only finite-dimensional real division algebras are the algebra of real numbers $\mathbb R$, the algebra of complex numbers $\mathbb C$, and the algebra of quaternions $\mathbb H$. We present a short proof which uses
Externí odkaz:
http://arxiv.org/abs/2405.01876
Let $R$ be a ring and let $n\ge 2$. We discuss the question of whether every element in the matrix ring $M_n(R)$ is a product of (additive) commutators $[x,y]=xy-yx$, for $x,y\in M_n(R)$. An example showing that this does not always hold, even when $
Externí odkaz:
http://arxiv.org/abs/2404.18116
Autor:
Brešar, Matej, Volčič, Jurij
Let $r$ be a nonconstant noncommutative rational function in $m$ variables over an algebraically closed field $K$ of characteristic 0. We show that for $n$ large enough, there exists an $X\in M_n(K)^m$ such that $r(X)$ has $n$ distinct and nonzero ei
Externí odkaz:
http://arxiv.org/abs/2401.11564
Autor:
Brešar, Matej
The paper surveys the theory of functional identities and its applications. No prior knowledge of the theory is required to follow the paper.
Comment: Accepted for publication in Bulletin of Mathematical Sciences
Comment: Accepted for publication in Bulletin of Mathematical Sciences
Externí odkaz:
http://arxiv.org/abs/2302.10451
Autor:
Brešar, Matej, Šemrl, Peter
Let $f$ bea noncommutativepolynomial of degree $m\ge 1$ over an algebraically closed field $F$ of characteristic $0$. If $n\ge m-1$ and $\alpha_1,\alpha_2,\alpha_3$ are nonzero elements from $F$ such that $\alpha_1+\alpha_2+\alpha_3=0$, then every tr
Externí odkaz:
http://arxiv.org/abs/2302.05106
Autor:
Brešar, Matej
Publikováno v:
Turkish J. Math. 46 (2022), 1691-1698 (special volume dedicated to Vesselin Drensky on his 70th birthday)
Let $A$ be an algebra over a field $F$ with {\rm char}$(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the condition t
Externí odkaz:
http://arxiv.org/abs/2209.13201
Autor:
Bajuk, Žan, Brešar, Matej
Publikováno v:
Linear Algebra Appl. 643, 2022, 125-136
An algebra $A$ is said to be two-sided zero product determined if every bilinear functional $\varphi:A\times A\to F$ satisfying $ \varphi(x,y)=0$ whenever $xy=yx=0$ is of the form $\varphi(x,y)=\tau_1(xy) + \tau_2(yx)$ for some linear functionals $\t
Externí odkaz:
http://arxiv.org/abs/2209.13194