Geodesic
Rings with Involution in which Every Trace is Nilpotent or Regular
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 130-137

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

A theorem of Marshall Osborn [15] states that a simple ring with involution of characteristic not 2 in which every non-zero symmetric element is invertible must be a division ring or the 2 × 2 matrices over a field. This result has been generalized in several directions. If R is semi-simple and every symmetric element (or skew, or trace) is invertible or nilpotent, then R must be a division ring, the 2 × 2 matrices over a field, or the direct sum of a division ring and its opposite [6; 8; 13; 16]. 
Montgomery, Susan. Rings with Involution in which Every Trace is Nilpotent or Regular. Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 130-137. doi: 10.4153/CJM-1974-014-7
@article{10_4153_CJM_1974_014_7,
     author = {Montgomery, Susan},
     title = {Rings with {Involution} in which {Every} {Trace} is {Nilpotent} or {Regular}},
     journal = {Canadian journal of mathematics},
     pages = {130--137},
     year = {1974},
     volume = {26},
     number = {1},
     doi = {10.4153/CJM-1974-014-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-014-7/}
}
TY  - JOUR
AU  - Montgomery, Susan
TI  - Rings with Involution in which Every Trace is Nilpotent or Regular
JO  - Canadian journal of mathematics
PY  - 1974
SP  - 130
EP  - 137
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-014-7/
DO  - 10.4153/CJM-1974-014-7
ID  - 10_4153_CJM_1974_014_7
ER  - 
%0 Journal Article
%A Montgomery, Susan
%T Rings with Involution in which Every Trace is Nilpotent or Regular
%J Canadian journal of mathematics
%D 1974
%P 130-137
%V 26
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-014-7/
%R 10.4153/CJM-1974-014-7
%F 10_4153_CJM_1974_014_7

[1] 1. Chacron, M. and Chacron, J., Rings with imolution of all whose symmetric elements are nilpotent or regular, Proc. Amer. Math. Soc. (to appear). Google Scholar

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

[3] 3. Erickson, T. S. and S. Montgomery, The prime radical in special Jordan rings, Trans. Amer. Math. Soc. 156 (1971), 155–164. Google Scholar

[4] 4. Herstein, I. N., Non-commutative rings (Carus Math. Monograph 15, M.A.A., 1968). Google Scholar

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

[6] 6. Herstein, I. N. and S. Montogmery, Invertible and regular elements in rings with involution, J. Algebra (to appear). Google Scholar

[7] 7. Jacobson, N., Structure of rings, Amer. Math. Soc. Colloquium Publ. 37 (1964). Google Scholar

[8] 8. Jacobson, N., Lectures on quadratic Jordan algebras (Tata Institute, Bombay, 1969). Google Scholar

[9] 9. Lanski, C., Nil subrings of Goldie rings are nilpotent, Can. J. Math. 21 (1969), 904–907. Google Scholar

[10] 10. Lanski, C., Rings with involution whose symmetric elements are regular, Proc. Amer. Math. Soc. 33 (1972), 264–270. Google Scholar

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

[12] 12. Martindale, W. S., III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. Google Scholar

[13] 13. McCrimmon, K., Quadratic Jordan algebras whose elements are all invertible or nilpotent, Proc. Amer. Math. Soc. 35 (1972), 309–316. Google Scholar

[14] 14. Montgomery, S., Lie structure of simple rings of characteristic 2, J. Algebra 15 (1970), 387–407. Google Scholar

[15] 15. Osborn, J. M., Jordan algebras of capacity 2, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 582–588. Google Scholar

[16] 16. Osborn, J. M., Jordan and associative rings with nilpotent and invertible elements, J. Algebra 15 (1970), 301–308. Google Scholar

Cité par Sources :