89 citations · 253 across the 20 of their papers we have counts for
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Representability of relatively free affine algebras over a Noetherian ring
Alexei Kanel-Belov, Louis Rowen, Uzi Vishne
Over the years questions have arisen about T-ideals of (noncommutative) polynomials. But when evaluating a noncentral polynomial in subalgebras of matrices, one often has little co…
On cogrowth function of algebras and its logarithmical gap
A. J. Kanel-Belov, I. A. Melnikov, I. V. Mitrofanov
Let be an associative algebra. A finite word over alphabet is {\it-reducible} if its image in is a -linear combination of length-lexi…
Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture
Alexei Kanel-Belov, Sergey Malev, Louis Rowen +1
Let be a polynomial in several non-commuting variables with coefficients in a field of arbitrary characteristic. It has been conjectured that for any , for multiline…
A short proof that the free associative algebra is Hopfian
Alexei Kanel-Belov, Louis Rowen, Jie-Tai Yu
A short proof is given of the fact that various classes of algebras including the free associative algebra are Hopfian, i.e., every epimorphism is an automorphism. This further sim…
Kemer's Theorem for Affine PI Algebras Over a Field of Characteristic Zero
Eli Aljadeff, Alexei Kanel-Belov, Yakov Karasik
We present a proof of Kemer's representability theorem for affine PI algebras over a field of characteristic zero.
The Grassmann algebra in arbitrary characteristic and generalized sign
Gal Dor, Alexei Kanel-Belov, Uzi Vishne
We define a generalization of the Grassmann algebra which is well-behaved over arbitrary commutative rings , even when is not invertible. In particular, t…
Hilbert series of PI relatively free G-graded algebras are rational functions
Eli Aljadeff, Alexei Kanel-Belov
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F<x_{1,g_1},...,x_{r,g_r}> be th…
Representability and Specht problem for G-graded algebras
Eli Aljadeff, Alexei Kanel-Belov
Let W be an associative PI algebra over a field F of characteristic zero, graded by a finite group G. Let id_{G}(W) denote the T-ideal of G-graded identities of W. We prove: 1. {[G…