Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T21:04:43.821Z Has data issue: false hasContentIssue false

Lie Action of Certain Skews in *-Rings

Published online by Cambridge University Press:  20 November 2018

M. Chacron*
Affiliation:
Carleton University, Ottawa, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A *-ring is an associative ring R with an anti-automorphism * of period 2 (involution). Call xR skew (symmetric) if x = - x* (x = x*) and let K(S) be the additive subgroup of all skews (symmetries). If [a, b] denotes the Lie product of a, bR (that is, ab — ba) and if [A, B] denotes the Lie product of the additive subgroups A and B of R (that is, the additive subgroup generated by [a, b], a and b ranging over A and B) then clearly [K, K] is an additive subgroup contained in K.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Baxter, W. E. and Haeusler, E. F., Generating submodules of simple rings with involution, Duke Math. J. 23 (1966), 595604.Google Scholar
2. Erickson, T., The Lie structure in prime rings with involution, J. of Algebra 21 (1972), 523534.Google Scholar
3. Herstein, I. N., Certain submodules of simple rings with involution, Duke Math. J. 24 (1967), 357364.Google Scholar
4. Herstein, I. N., Certain submodules of simple rings with involution II, Can. J. Math. 27 (1975), 629635.Google Scholar
5. Herstein, I. N., Lecture on rings with involution (University of Chicago Press, Chicago, 1976).Google Scholar
6. Herstein, I. N., Topics in ring theory (University of Chicago, Chicago, 1969).Google Scholar
7. Herstein, I. N., On the Lie structure of an associative ring, J. of Algebra 21 (1970), 561571.Google Scholar