Annihilator condition of a pair of derivations in prime and semiprime rings

作者：Dhara Basudeb^*; Argac Nurcan^*; Pradhan Krishna Gopal^*

来源：Indian Journal of Pure and Applied Mathematics, 2016, 47(1): 111-124.

DOI：10.1007/s13226-015-0166-z

• Prime ring
• derivation
• extended centroid
• Martindale quotient ring

Let n be a fixed positive integer, R be a prime ring, D and G two derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 not equal a a R such that a(D(u)u (n) -u (n) G(u)) = 0 for all u a L, where n a parts per thousand yen 1 is a fixed integer. Then one of the following holds: D = G = 0, unless R satisfies s (4);
char (R) not equal 2, R satisfies s (4), n is even and D = G;
char (R) not equal 2, R satisfies s (4), n is odd and D and G are two inner derivations induced by b, c respectively such that b + c a C;
char (R) = 2 and R satisfies s (4).
We also investigate the case when R is a semiprime ring.

• 出版日期2016-3