Matej Brešar

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7 papers · 1 filter

math.RA2024★ 1 cited

Products of commutators in matrix rings

Matej Brešar, Eusebio Gardella, Hannes Thiel

Let $R$ be a ring and let $n \geq 2$ . We discuss the question of whether every element in the matrix ring $M_{n} (R)$ is a product of (additive) commutators $[x, y] = x y - y x$ , for $x,y\in M…

math.RA2023

f-zpd algebras and a multilinear Nullstellensatz

Ž. Bajuk, M. Brešar, P. Fagundes +1

Let $f = f (x_{1}, \dots, x_{m})$ be a multilinear polynomial over a field $F$ . An $F$ -algebra $A$ is said to be $f$ -zpd ( $f$ -zero product determined) if every $m$ -linear functional $φ\colo…

math.RA2023★ 1 cited

Functional identities and their applications

Matej Brešar

The paper surveys the theory of functional identities and its applications. No prior knowledge of the theory is required to follow the paper.

math.RA2023

The Waring Problem for Matrix Algebras, II

Matej Brešar, Peter Šemrl

Let $f$ bea noncommutativepolynomial of degree $m \geq 1$ over an algebraically closed field $F$ of characteristic $0$ . If $n \geq m - 1$ and $α_{1}, α_{2}, α_{3}$ are nonzero elements from $F$ …

math.RA2012

On Lie and associative algebras containing inner derivations

M. Brešar, Š. Špenko

We describe subalgebras of the Lie algebra $\mf{gl}(n^2)$ that contain all inner derivations of $A = M_{n} (F)$ (where $n \geq 5$ and $F$ is an algebraically closed field of characteristi…

math.RA2012

Maps preserving zeros of a polynomial

J. Alaminos, M. Brešar, Š. Špenko +1

Let $\A$ be an algebra and let $f (x_{1}, ..., x_{d})$ be a multilinear polynomial in noncommuting indeterminates $x_{i}$ . We consider the problem of describing linear maps $ϕ:\A\to \A$ tha…