3 papers
math.RA2022
On the existence of left and right eigenvalues
Bamdad R. Yahaghi
In this note, we consider arbitrary finite-dimensional real algebras containing a copy of complex numbers. It is proved that matrices with entries from an arbitrary finite-dimensio…
math.RA2018
Burnside's theorem in the setting of general fields
Heydar Radjavi, Bamdad R. Yahaghi
We extend a well-known theorem of Burnside in the setting of general fields as follows: for a general field the matrix algebra is the only algebra in which is…
math.RA2016
An extension of a theorem of Kaplansky
Heydar Radjavi, Bamdad R. Yahaghi
A theorem of Kaplansky asserts that a semigroup of matrices with entries from a field whose members all have singleton spectra is triangularizable. Indeed, Kaplansky's Theorem unif…