Lie Ideals in Associative Algebras
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 10-15

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

It is shown that in a certain extensive class of algebras one can associate with each Lie ideal a corresponding associative ideal which facilitates the study of Lie ideals, especially for simple algebras. We apply this construction to obtain new, simpler proofs of some known results of Herstein [10] and others on the Lie structure of associative rings.
DOI : 10.4153/CMB-1984-002-0
Mots-clés : 16A68, 17B60
Murphy, G. J. Lie Ideals in Associative Algebras. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 10-15. doi: 10.4153/CMB-1984-002-0
@article{10_4153_CMB_1984_002_0,
     author = {Murphy, G. J.},
     title = {Lie {Ideals} in {Associative} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {10--15},
     year = {1984},
     volume = {27},
     number = {1},
     doi = {10.4153/CMB-1984-002-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-002-0/}
}
TY  - JOUR
AU  - Murphy, G. J.
TI  - Lie Ideals in Associative Algebras
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 10
EP  - 15
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-002-0/
DO  - 10.4153/CMB-1984-002-0
ID  - 10_4153_CMB_1984_002_0
ER  - 
%0 Journal Article
%A Murphy, G. J.
%T Lie Ideals in Associative Algebras
%J Canadian mathematical bulletin
%D 1984
%P 10-15
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-002-0/
%R 10.4153/CMB-1984-002-0
%F 10_4153_CMB_1984_002_0

[1] 1. Anderson, J., Commutators of compact operators. Journal für die reine und angewandte Mathematik, Band 291 (1977) 128-132. Google Scholar

[2] 2. Brown, A. and Pearcy, C., Structure of commutators of operators. Ann of Math. (2) 82 (1965) 112-127. Google Scholar

[3] 3. Calkin, J. N., Two-sided ideals and congruences in the ring of bounded operators in Hilbert space. Ann of Math, 42 (1941) 839-873. Google Scholar

[4] 4. Harpe, P. de la, The algebra of compact operators does not have any finite-codimensional ideal, Studia Math 66 (1979), 33-36. Google Scholar

[5] 5. Faith, C., Algebra: Rings, Modules and Categories I. Springer, 1973. Google Scholar

[6] 6. Fillmore, P., Sum of operators with square zero. Acta Sci. Math. 28 (1967) 285-288. Google Scholar

[7] 7. Fillmore, P., On products of symmetries. Canad. J. Math. 18 (1966) 897-900. Google Scholar

[8] 8. Fong, C. K., Meiers, C. R. and Sourour, A. R., Lie and Jordan ideals of operators on Hilbert space (preprint). Google Scholar

[9] 9. Halmos, P. and Kakutani, S., Products of symmetries. Bull. Amer. Math. Soc. 64 (1958) 77-78. Google Scholar

[10] 10. Herstein, I. N., Topics in Ring Theory. University of Chicago, 1969. Google Scholar

[11] 11. Murphy, G. J. and Radjavi, H., Associative and Lie subalgebras of finite codimension (to appear in Studia Math.). Google Scholar

[12] 12. Pearcy, C. and Topping, D., Sums of small numbers of idempotents. Michigan Math. J. 14 (1967) 453-465. Google Scholar

[13] 13. Topping, D., Lectures on von Neumann Algebras. Van Nostrand, 1971. Google Scholar

Cité par Sources :