Geodesic
Invariant Subrings in Rings with Involution
Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 85-94

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

The purpose of this paper is to consider, in rings with involution, the structure of those subrings which are invariant under Lie commutation with [K, K]. Our goal is to find conditions which force such subrings to contain a noncentral ideal of the ring. Of course, the subring itself may lie in the center. Orders in 4 × 4 matrix rings over fields are known to provide examples of invariant subrings which are not central and contain no ideal (see [1, 40] or [5]). Except for subdirect products of these two kinds of “counter-examples”, we show that in semi-prime rings, invariant subrings do contain noncentral ideals. This generalizes work of Herstein [4] in two directions by considering semi-prime rings rather than simple rings, and by using [K, K] instead of K. 
Lanski, Charles. Invariant Subrings in Rings with Involution. Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 85-94. doi: 10.4153/CJM-1978-007-8
@article{10_4153_CJM_1978_007_8,
     author = {Lanski, Charles},
     title = {Invariant {Subrings} in {Rings} with {Involution}},
     journal = {Canadian journal of mathematics},
     pages = {85--94},
     year = {1978},
     volume = {30},
     number = {1},
     doi = {10.4153/CJM-1978-007-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-007-8/}
}
TY  - JOUR
AU  - Lanski, Charles
TI  - Invariant Subrings in Rings with Involution
JO  - Canadian journal of mathematics
PY  - 1978
SP  - 85
EP  - 94
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-007-8/
DO  - 10.4153/CJM-1978-007-8
ID  - 10_4153_CJM_1978_007_8
ER  - 
%0 Journal Article
%A Lanski, Charles
%T Invariant Subrings in Rings with Involution
%J Canadian journal of mathematics
%D 1978
%P 85-94
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-007-8/
%R 10.4153/CJM-1978-007-8
%F 10_4153_CJM_1978_007_8

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

[2] 2. Herstein, I. N., On the Lie structure of an associative ring, J. Algebra 14 (1970), 561–571. Google Scholar

[3] 3. Herstein, I. N., A unitary version of the Brauer-Cartan-Hua theorem, J. Algebra 32 (1974), 554–560. 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. Lanski, C., Lie structure in semi-prime rings with involution, Comm. in Alg. 4 (1976), 731–746. Google Scholar

[6] 6. Lanski, C. and Montgomery, S., Lie structure of prime rings of characteristic 2, Pacific J. Math. 42 (1972), 117–136. Google Scholar

Cité par Sources :