66 citations · 325 across the 49 of their papers we have counts for
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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…
Supertropical Quadratic Forms I
Zur Izhakian, Manfred Knebusch, Louis Rowen
We initiate the theory of a quadratic form over a semiring . As customary, one can write where is a companion bilinear form. But in con…
Specht's problem for associative affine algebras over commutative Noetherian rings
Alexei Belov-Kanel, Louis Rowen, Uzi Vishne
In a series of papers \cite{BRV1}, \cite{BRV2}, \cite{BRV3} we introduced full quivers and pseudo-quivers of representations of algebras, and used them as tools in describing PI-va…
The Jacobian Conjecture, together with Specht and Burnside-type problems
Alexei Belov, Leonid Bokut, Louis Rowen +1
We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovi…
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…