Geodesic
Lie Action of Certain Skews in *-Rings
Canadian journal of mathematics, Tome 30 (1978) no. 4, pp. 700-710

Voir la notice de l'article provenant de la source Cambridge University Press

A *-ring is an associative ring R with an anti-automorphism * of period 2 (involution). Call x ∈ R 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, b ∈ R (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. 
Chacron, M. Lie Action of Certain Skews in *-Rings. Canadian journal of mathematics, Tome 30 (1978) no. 4, pp. 700-710. doi: 10.4153/CJM-1978-061-9
@article{10_4153_CJM_1978_061_9,
     author = {Chacron, M.},
     title = {Lie {Action} of {Certain} {Skews} in {*-Rings}},
     journal = {Canadian journal of mathematics},
     pages = {700--710},
     year = {1978},
     volume = {30},
     number = {4},
     doi = {10.4153/CJM-1978-061-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-061-9/}
}
TY  - JOUR
AU  - Chacron, M.
TI  - Lie Action of Certain Skews in *-Rings
JO  - Canadian journal of mathematics
PY  - 1978
SP  - 700
EP  - 710
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-061-9/
DO  - 10.4153/CJM-1978-061-9
ID  - 10_4153_CJM_1978_061_9
ER  - 
%0 Journal Article
%A Chacron, M.
%T Lie Action of Certain Skews in *-Rings
%J Canadian journal of mathematics
%D 1978
%P 700-710
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-061-9/
%R 10.4153/CJM-1978-061-9
%F 10_4153_CJM_1978_061_9

[1] 1. Baxter, W. E. and Haeusler, E. F., Generating submodules of simple rings with involution, Duke Math. J. 23 (1966), 595–604. Google Scholar

[2] 2. Erickson, T., The Lie structure in prime rings with involution, J. of Algebra 21 (1972), 523–534. Google Scholar

[3] 3. Herstein, I. N., Certain submodules of simple rings with involution, Duke Math. J. 24 (1967), 357–364. Google Scholar

[4] 4. Herstein, I. N., Certain submodules of simple rings with involution II, Can. J. Math. 27 (1975), 629–635. Google Scholar

[5] 5. Herstein, I. N., Lecture on rings with involution (University of Chicago Press, Chicago, 1976). Google Scholar

[6] 6. Herstein, I. N., Topics in ring theory (University of Chicago, Chicago, 1969). Google Scholar

[7] 7. Herstein, I. N., On the Lie structure of an associative ring, J. of Algebra 21 (1970), 561–571. Google Scholar

Cité par Sources :