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Two-sided zero product determined algebras
Žan Bajuk, Matej Brešar
An algebra is said to be two-sided zero product determined if every bilinear functional satisfying whenever is of the form $φ(x,y)=τ_1(…
The Waring Problem for Matrix Algebras
Matej Bresar, Peter Semrl
If a noncommutative polynomial is neither an identity nor a central polynomial of $\mathcal A=M_n(\C)$, then every trace zero matrix in can be written as a sum of…
On, Around, and Beyond Frobenius' Theorem on Division Algebras
Matej Brešar, Victor S. Shulman
Frobenius' Theorem states that the algebra of quaternions is, besides the fields of real and complex numbers, the only finite-dimensional real division algebra. We firs…
On locally complex algebras and low-dimensional Cayley-Dickson algebras
Matej Bresar, Peter Semrl, Spela Spenko
The paper begins with short proofs of classical theorems by Frobenius and (resp.) Zorn on associative and (resp.) alternative real division algebras. These theorems characterize th…
An elementary approach to Wedderburn's structure theory
Matej Bresar
Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.