半素环上对称逆双导lie理想的一些结果

IF 0.5 Q3 MATHEMATICS Facta Universitatis-Series Mathematics and Informatics Pub Date : 2021-07-30 DOI:10.22190/FUMI200708023K

Emine Koc Sogutcu, Ö. Gölbasi

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摘要

设R是一个半素环，U是R和D的平方闭李理想:R R !R是对称逆双导，d是d的迹。本文证明R交换环的成立条件为:i) d(U) = (0);(二)Z d (U);Iii)[d (x)];y] 2 Z;iv)d(x) y 2z;v) d ([x;y]) [d (x);y] 2 Z;vi)d (x)y (d(x)y) 2z;(七)d ([x;y])d(x)y 2zviii)d(x)y [d(x);y] 2 Z;d(x) y [d(y);x] 2 Z;x) d ([x;(d(x) Y) [d(Y);[x] 2zxi)[d(x);y] [g (y);x] 2 Z;对于所有x;y 2 U;G: R R R !R是对称逆双导使得g是的迹

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SOME RESULTS ON LIE IDEALS WITH SYMMETRIC REVERSE BI-DERIVATIONS IN SEMIPRIME RINGS I

Let R be a semiprime ring, U a square-closed Lie ideal of R and D : R R ! R a symmetric reverse bi-derivation and d be the trace of D: In the present paper, we shall prove that R commutative ring if any one of the following holds: i) d(U) = (0); ii)d(U) Z; iii)[d (x) ; y] 2 Z; iv)d(x)oy 2 Z; v)d ([x; y])[d(x); y] 2 Z; vi)d (x y)(d(x)y) 2 Z; vii)d ([x; y])d(x)y 2 Z viii)d (x y) [d(x); y] 2 Z; ix)d(x) y [d(y); x] 2 Z; x)d([x; y]) (d(x) y) [d(y); x] 2 Z xi)[d(x); y] [g(y); x] 2 Z; for all x; y 2 U; where G : R R ! R is symmetric reverse bi-derivations such that g is the trace of

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Facta Universitatis-Series Mathematics and Informatics MATHEMATICS-

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