2018
Том 70
№ 7

All Issues

Fošner A.

Articles: 2
Brief Communications (English)

Generalized higher derivations on algebras

Fošner A.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 10. - pp. 1429-1436

We study the structure of generalized higher derivations on an algebra ${\scr A}$ and show that there exists a one-to-one correspondence between the set of all generalized higher derivations $\{ G_k\}^n_{k =0}$ on ${\scr A}$ with $G_0 = I$ and the set of all sequences $\{ g_k\}^n_{k = 0}$ of generalized derivations on ${\scr A}$ with $g_0 = 0$.

Brief Communications (English)

Remarks on Certain Identities with Derivations on Semiprime Rings

Baydar N., Fošner A., Strašek R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1436–1440

Let $n$ be a fixed positive integer, let $R$ be a $(2n)!$ -torsion-free semiprime ring, let $\alpha$ be an automorphism or an anti-automorphism of $R$, and let $D_1 , D_2 : R → R$ be derivations. We prove the following result: If $(D_1^2 (x) + D_2(x))^n  ∘ α(x)^n  = 0 $ holds for all $x Є R$, then $D_1 = D_2 = 0$. The same is true if $R$ is a 2-torsion free semiprime ring and F(x) ° β(x) = 0 for all x ∈ R, where $F(x) = (D_1^2 (x) + D_2(x)) ∘ α(x),\; x ∈ R$, and $β$ is any automorphism or antiautomorphism on $R$.