On Jordan Structure in Semiprime Rings
Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 1067-1072
Voir la notice de l'article provenant de la source Cambridge University Press
A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and has proved that if R is a semiprime ring of characteristic different from 2 and V is an additive subgroup of R such that [V, U] ⊂ V, where U is a Lie ideal of R, then either [V, U] = 0 or V ⊃ [M, R] ≠ 0 where M is an ideal of R. In this paper our object is to prove the following.
Awtar, Ram. On Jordan Structure in Semiprime Rings. Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 1067-1072. doi: 10.4153/CJM-1976-105-x
@article{10_4153_CJM_1976_105_x,
author = {Awtar, Ram},
title = {On {Jordan} {Structure} in {Semiprime} {Rings}},
journal = {Canadian journal of mathematics},
pages = {1067--1072},
year = {1976},
volume = {28},
number = {5},
doi = {10.4153/CJM-1976-105-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-105-x/}
}
[1] 1. Herstein, I. N., On the Lie and Jordan rings of a simple associative ring, Amer. J. Math. 77 (1955), 279–285. Google Scholar
[2] 2. Herstein, I. N., Topics in ring theory (University of Chicago Press, Chicago, 1969). Google Scholar
3, On the Lie structure of associative rings, J. Algebra 14 (1970), 561–571. Google Scholar
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