TY  - JOUR
TI  - Some identities involving multiplicative semiderivations on ideals
AB  - Let $R$ be a prime ring and $I$ be a nonzero ideal of $R.$ A mapping $d:Rrightarrow R$ is called a multiplicative semiderivation if there exists a function $g:Rrightarrow R$ such that (i) $d(xy)=d(x)g(y)+xd(y)=d(x)y+g(x)d(y)$ and (ii) $d(g(x))=g(d(x))$ hold for all $x,yin R.$ In the present paper, we shall prove that $[x,d(x)]=0,$ for all $xin I$ if any of the followings holds: i) $d(xy)pm xyin Z,$ ii) $d(xy)pm yxin Z,$ iii) $d(x)d(y)pm xyin Z,$ iv) $d(xy)pm d(x)d(y)in Z,$ viii) $d(xy)pm d(y)d(x)in Z,$ for all $x,yin I.$ Also, we show that $R$ must be commutative if $d(I)subseteq Z.$
AU  - Gölbaşı, Öznur
AU  - bedir, zeliha
DO  - 10.15672/hujms.650600
PY  - 2021
JO  - Hacettepe Journal of Mathematics and Statistics
VL  - 50
IS  - 4
SN  - 1303-5010
SP  - 963
EP  - 969
DB  - TRDizin
UR  - http://search/yayin/detay/493993
ER  -