11 papers
Fully non-zero matrices and generators of full algebras of operators
Laurent W. Marcoux, Heydar Radjavi, Bamdad R. Yahaghi +1
In a wide variety of fields, every non-scalar matrix is similar to a matrix all of whose entries are non-zero. We give extensions of this result, including some in the division…
Spectrum in alternative topological algebras and a new look at old theorems
Bamdad R. Yahaghi
In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over genera…
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…
Extensions of the fundamental theorem of algebra
Bamdad R. Yahaghi
In this paper motivated by the celebrated fundamental theorem of algebra and its standard proof utilizing Liouville's Theorem, we prove the fundamental theorem of algebra type resu…
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…
Burnside type theorems in real and quaternion settings
Bamdad R. Yahaghi
In this note, we consider irreducible semigroups of real, complex, and quaternionic matrices with real spectra. We prove Burnside type theorems in the settings of reals and quatern…
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…
A theorem of Kaplansky revisited
Heydar Radjavi, Bamdad R. Yahaghi
We present a new and simple proof of a theorem due to Kaplansky which unifies theorems of Kolchin and Levitzki on triangularizability of semigroups of matrices. We also give two di…
On modules of linear transformations
M. Rahimi-Alangi, Bamdad R. Yahaghi
Let be a division ring, and vector spaces over , and the -${\mathcal L(\mathcal V)…
On nest modules of matrices over division rings
M. Rahimi-Alangi, Bamdad R. Yahaghi
Let , be a division ring, and denote the bimodule of all matrices with entries from . First, we characterize one-side…
Theorems of Burnside and Wedderburn revisited
Bamdad R. Yahaghi
We approach celebrated theorems of Burnside and Wedderburn via simultaneous triangularization. First, for a general field , we prove that is the only irrreducible subal…