66 citations · 207 across the 19 of their papers we have counts for
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Algebro-geometric proof of Christoph's Theorem
Sergey Malev, Anastasiia Zhilina
In this paper an algebraic proof of Christoph's theorem is provided. This theorem from algebraic-geometry is about the existence of a finite automaton for computing coefficient of…
The images of multilinear and semihomogeneous polynomials on the algebra of octonions
Alexei Kanel-Belov, Sergey Malev, Coby Pines +1
The generalized L'vov-Kaplansky conjecture states that for any finite-dimensional simple algebra the image of a multilinear polynomial on is a vector space. In this paper w…
The images of Lie polynomials evaluated on matrices
Alexei Kanel-Belov, Sergey Malev, Louis Rowen
Kaplansky asked about the possible images of a polynomial in several noncommuting variables. In this paper we consider the case of a Lie polynomial. We describe all the pos…
Power-central polynomials on matrices
Alexei Kanel-Belov, Sergey Malev, Louis Rowen
Any multilinear non-central polynomial (in several noncommuting variables) takes on values of degree in the matrix algebra over an infinite field . The polynomi…
The images of non-commutative polynomials evaluated on matrices over an arbitrary field
Sergey Malev
Let be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field . Kaplansky conjectured that for any , the image of evaluat…
The images of multilinear polynomials evaluated on matrices
Alexei Kanel-Belov, Sergey Malev, Louis Rowen
Let be a multilinear polynomial in several noncommuting variables, with coefficients in a algebraically closed field of arbitrary characteristic. In this paper we classify…