2 citations · 5 across the 21 of their papers we have counts for
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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…
Z2-graded Cayley-Hamilton trace identities in M_{n}(E)
Szilvia Homolya, Jeno Szigeti
We show, how the combination of the Cayley-Hamilton theorem and a certain companion matrix construction can be used to derive Z2-graded trace identities in M_{n}(E).
A power Cayley-Hamilton identity for nxn matrices over a Lie nilpotent ring of index k
Jeno Szigeti, Szilvia Szilagyi, Leon van Wyk
For an nxn matrix A over a Lie nilpotent ring R of index k, we prove that an invariant "power" Cayley-Hamilton identity of degree (n^2)2^{k-2} holds. The right coefficients are not…
A Constructive Elementary Proof of the Skolem-Noether Theorem for Matrix Algebras
Jeno Szigeti, Leon van Wyk
We give a constructive elementary proof for the fact that any K-automorphism of the full nxn matrix algebra over a field K is conjugation by some invertible nxn matrix A over K.
The maximum dimension of a Lie nilpotent subalgebra of M_{n}(F) of index m
J. Szigeti, J. van den Berg, L. van Wyk +1
The main result of this paper is the following: if F is any field and R is any F-subalgebra of the algebra of nxn matrices over F with Lie nilpotence index m, then the F-dimension…
Which self-maps appear as lattice endomorphisms?
Jeno Szigeti
Let f be a self-map of the set A. We give a necessary and sufficient condition for the existence of a lattice structure on A such that f becomes a lattice endomorphism with respect…