2 citations · 5 across the 21 of their papers we have counts for
25 papers
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…
Power-conjugate equations in symmetric groups
Szilvia Homolya, Jenő Szigeti
We investigate the solutions of the conjugate equation aya^(-1)=y^e in the symmetric group S_{n}. Here a is a fixed (constant), e is an integer exponent and y is a single unknown p…
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.
Functions realising as abelian group automorphisms
B-E de Klerk, JH Meyer, J Szigeti +1
Let be a set and a bijective function. Necessary and sufficient conditions on are determined which makes it possible to endow with a binary operation…