17 citations · 22 across the 6 of their papers we have counts for
8 papers
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…
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…
Idempotents and structures of rings
P. N. Anh, G. F. Birkenmeier, L. van Wyk
We study a ring containing a complete set of orthogonal idempotents as a generalized matrix ring via its Peirce decomposition. We focus on the case where some of the underlying bim…
On Lie nilpotent rings and Cohen's Theorem
Jeno Szigeti, Leon van Wyk
We study certain (two-sided) nil ideals and nilpotent ideals in a Lie nilpotent ring R. Our results lead us to showing that the prime radical rad(R) of R comprises the nilpotent el…
Matrix representations of finitely generated Grassmann algebras and some consequences
László Márki, Johan Meyer, Jenő Szigeti +1
We prove that the m-generated Grassmann algebra can be embedded into a 2^{m-1}x2^{m-1} matrix algebra over a factor of a commutative polynomial algebra in m indeterminates. Cayley-…
Determinants for nxn matrices and the symmetric Newton formula in the 3x3 case
J. Szigeti, L. van Wyk
One of the aims of this paper is to provide a short survey on the Z2-graded, the symmetric and the left (right) generalizations of the classical determinant theory for square matri…
Jordan Derivations and Antiderivations of Generalized Matrix Algebras
Yanbo Li, Leon van Wyk, Feng Wei
Let $\mathcal{G}=[A & M N & B]$ be a generalized matrix algebra defined by the Morita context . In this article we mainly study the question of…
Algebras generated by two quadratic elements
Vesselin Drensky, Jeno Szigeti, Leon van Wyk
Let K be a field of any characteristic and let R be an algebra generated by two elements satisfying quadratic equations. Then R is a homomorphic image of F=K<x,y | x^2+ax+b=0,y^2+c…