3 citations · 4 across the 4 of their papers we have counts for
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The structure of subalgebras of full matrix algebras over a field satisfying the identity [x_1, y_1][x_2, y_2] ... [x_q, y_q] = 0
Pawel Matras, Leon van Wyk, Michal Ziembowski
A subalgebra of the full matrix algebra Mn(K), K a field, satisfying the identity [x1, y1][x2, y2]...[xq, yq] = 0 is called a Dq subalgebra of Mn(K). In the paper we deal with the…
Lie properties in associative algebras
Szilvia Homolya, Jeno Szigeti, Leon van Wyk +1
Let K be a field, then we exhibit two matrices in the full nxn matrix algebra M_{n}(K) which generate M_{n}(K) as a Lie K-algebra with the commutator Lie product. We also study Lie…
On Radicals of Ore Extensions and Related Questions
Be'eri Greenfeld, Agata Smoktunowicz, Michal Ziembowski
We answer several open questions and establish new results concerning differential and skew polynomial ring extensions, with emphasis on radicals. In particular, we prove the follo…
Differential poynomial rings over locally nilpotent rings need not be Jacobson radical
Agata Smoktunowicz, Michal Ziembowski
We answer a question by Shestakov on the Jacobson radical in differential polynomial rings. We show that if R is a locally nilpotent ring with a derivation D then R[X;D] need not b…