Szilvia Homolya
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View article: Digital technology in university mathematics education
Digital technology in university mathematics education Open
The development of the technology in the past decade, called Industry 4.0 has an effect on every segment of everyday life, as well as on education. However the use of digital technology in education was launched earlier and it has become a…
View article: The results of the university competence measurement in mathematics in the view of the tasks
The results of the university competence measurement in mathematics in the view of the tasks Open
Experience shows that students applying to higher education have a highly differentiated knowledge of mathematics.They come from different types of secondary school, and it is not a general requirement to have an advanced level secondary s…
View article: A "power" conjugate equation in the symmetric group
A "power" conjugate equation in the symmetric group Open
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^…
View article: Lie properties in associative algebras
Lie properties in associative algebras Open
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 alge…
View article: Solving equations in the symmetric group
Solving equations in the symmetric group Open
We investigate the solutions of the conjugate equation aya^(-1)=y^2 in the symmetric group S_{n}. Here a is a fixed (constant) and y is a single unknown permutation (in S_{n}). It turns out that the existence of a non-trivial solution y he…
View article: Power-conjugate equations in symmetric groups
Power-conjugate equations in symmetric groups Open
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…
View article: Z2-graded Cayley-Hamilton trace identities in M_{n}(E)
Z2-graded Cayley-Hamilton trace identities in M_{n}(E) Open
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).