Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Szigeti, Jenő"'
Autor:
Homolya, Szilvia, Szigeti, Jenő
First we consider the solutions of the general "cubic" equation a_{1}x^{r1}a_{2}x^{r2}a_{3}x^{r3}=1 (with r1,r2,r3 in {1,-1}) in the symmetric group S_{n}. In certain cases this equation can be rewritten as aya^{-1}=y^{2} or as aya^{-1}=y^{-2}, where
Externí odkaz:
http://arxiv.org/abs/2202.03921
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 centralizers of a not necessarily commutative unitary algebra and obt
Externí odkaz:
http://arxiv.org/abs/2110.02534
Autor:
Homolya, Szilvia, Szigeti, Jenő
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 permutation (in S_{n}). It turns out that the existence of a non-trivia
Externí odkaz:
http://arxiv.org/abs/2104.03593
Autor:
Homolya, Szilvia, Szigeti, Jeno
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).
Externí odkaz:
http://arxiv.org/abs/2004.12101
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 uniquely determined by A, and the cosets lambda_i+D, with D the doubl
Externí odkaz:
http://arxiv.org/abs/1909.10210
Autor:
Szigeti, Jeno, van Wyk, Leon
Publikováno v:
American Mathematical Monthly 124: pp. 966-968. (2017)
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.
Externí odkaz:
http://arxiv.org/abs/1810.08368
Publikováno v:
In Journal of Environmental Management 15 January 2022 302 Part B
Autor:
Szigeti, Jeno
Let R be a Lie nilpotent algebra of index k over a field K of characteristic zero. If G is an n-element subgroup of Aut(R) of the K-automorphisms, then we prove that R is right integral over Fix(G) of degree n^k. In the presence of a primitive n-th r
Externí odkaz:
http://arxiv.org/abs/1501.07104
Autor:
Szigeti, Jeno
Publikováno v:
Discrete Mathematics, Vol. 321 (2014), 53-56
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 to this structure.
Comment: arXiv admin note: substantial text o
Comment: arXiv admin note: substantial text o
Externí odkaz:
http://arxiv.org/abs/1501.04043
Autor:
Szigeti, Jeno, van Wyk, Leon
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 elements of R, and that if L is a left ideal of R, then L+rad(R) is a tw
Externí odkaz:
http://arxiv.org/abs/1501.00787