Turkish Journal of Mathematics
DOI
10.3906/mat-2002-24
Abstract
Let $R$ be a prime ring with center $Z(R)$ and an automorphism $\alpha.$ A mapping $\delta:R\to R$ is called multiplicative skew derivation if $\delta(xy)=\delta(x)y+ \alpha(x)\delta(y)$ for all $x,y\in R$ and a mapping $F:R\to R$ is said to be multiplicative (generalized)-skew derivation if there exists a unique multiplicative skew derivation $\delta$ such that $F(xy)=F(x)y+\alpha(x)\delta(y)$ for all $x,y\in R.$ In this paper, our intent is to examine the commutativity of $R$ involving multiplicative (generalized)-skew derivations that satisfy the following conditions: (i) $F(x^{2})+x\delta(x)=\delta(x^{2})+xF(x)$, (ii) $F(x\circ y)=\delta(x\circ y)\pm x\circ y$, (iii) $F([x,y])=\delta([x,y])\pm [x,y]$, (iv) $F(x^{2})=\delta(x^{2})$, (v) $F([x,y])=\pm x^{k}[x,\delta(y)]x^{m}$, (vi) $F(x\circ y)=\pm x^{k}(x\circ\delta(y))x^{m}$, (vii) $F([x,y])=\pm x^{k}[\delta(x),y]x^{m}$, (viii) $F(x\circ y)=\pm x(\delta(x)\circ y)x^{m}$ for all $x,y\in R.$
First Page
1401
Last Page
1411
Recommended Citation
SANDHU, GURNINDER SINGH and CAMCI, DİDEM KARALARLIOĞLU
(2020)
"Some results on prime rings with multiplicative derivations,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 23.
https://doi.org/10.3906/mat-2002-24
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/23
