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On Jordan Structure in Semiprime Rings

Published online by Cambridge University Press:  20 November 2018

Ram Awtar
Ram Awtar*
Affiliation:
Aligarh Muslim University, Aligarh, U.P., India
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1067 - 1072
Copyright
Copyright © Canadian Mathematical Society 1976

References

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. 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