66 citations · 325 across the 49 of their papers we have counts for
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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…
A tropical Krull-Schmidt theorem
Tal Perri, Louis Rowen
We develop some algebraic structure notions such as composition series and convexity degree, along with some notions holding a geometric interpretation, like reducibility and hyper…
Congruences and coordinate semirings of tropical varieties
Zur Izhakian, Louis Rowen
In this paper we present two intrinsic algebraic definitions of tropical variety motivated by the classical Zariski correspondence, one utilizing the algebraic structure of the coo…
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…