ON AN EXTENSION OF A RESULT OF HERSTEIN
2013 ◽
Vol 12
(08)
◽
pp. 1350051
A derivation of an associative ring R is an additive map satisfying T(xy) = T(x)y + xT(y) for all x, y in R. We study rings with a derivation T satisfying Herstein's condition [T(R), T(R)] = 0. (The commutator [u, v] is defined by: [u, v] = uv - vu.) This work studies the structure of the ideal I generated by T(R). We show that I3 is in the center of R, and we show that R has an ideal K which is contained in the kernel of T, K2 = 0, and [T(R/K), R/K] generates a trivial ideal of R/K.
1980 ◽
Vol 23
(3)
◽
pp. 299-303
◽
Keyword(s):
1996 ◽
Vol 54
(1)
◽
pp. 41-54
◽
2013 ◽
Vol 89
(3)
◽
pp. 503-509
Keyword(s):
1970 ◽
Vol 22
(6)
◽
pp. 1097-1100
◽
1975 ◽
Vol 27
(2)
◽
pp. 434-438
◽
Keyword(s):
2014 ◽
Vol 13
(05)
◽
pp. 1350151
◽
1970 ◽
Vol 28
◽
pp. 174-175
1974 ◽
Vol 32
◽
pp. 330-331