Homoderivations in Prime Rings

Authors : Ayşe ENGİN, Neşet AYDIN

Pages : 23-34

Doi:10.53570/jnt.1258402

View : 55 | Download : 68

Publication Date : 2023-06-30

Article Type : Research Paper

Abstract :The study consists of two parts. The first part shows that if $h_{1}insert ignore into journalissuearticles values(x);h_{2}insert ignore into journalissuearticles values(y);=h_{3}insert ignore into journalissuearticles values(x);h_{4}insert ignore into journalissuearticles values(y);$, for all $x,y\\in R$, then $ h_{1}=h_{3}$ and $h_{2}=h_{4}$. Here, $h_{1},h_{2},h_{3},$ and $h_{4}$ are zero-power valued non-zero homoderivations of a prime ring $R$. Moreover, this study provide an explanation related to $h_{1}$ and $h_{2}$ satisfying the condition $ah_{1}+h_{2}b=0$. The second part shows that $L\\subseteq Z$ if one of the following conditions is satisfied: $i. hinsert ignore into journalissuearticles values(L);=insert ignore into journalissuearticles values(0);$, $ ii. hinsert ignore into journalissuearticles values(L);\\subseteq Z$, $iii. hinsert ignore into journalissuearticles values(xy);=xy$, for all $x,y\\in L$, $iv. hinsert ignore into journalissuearticles values(xy);=yx$, for all $x,y\\in L$, or $v. hinsert ignore into journalissuearticles values([x,y]);=0$, and for all $x,y\\in L$. Here, $R$ is a prime ring with a characteristic other than $2$, $h$ is a homoderivation of $R$, and $L$ is a non-zero square closed Lie ideal of $R$.
Keywords : Prime rings, Lie ideals, homoderivations