Geodesic
Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution
Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 1045-1054

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

Let R be a prime ring with invoution *, of characteristic 0, with skew elements K and extended centroid C. Let a ∈ K be such that (ad a)n =0 on K. It is shown that one of the following possibilities holds: (a) R is an order in a 4-dimensional central simple algebra, (b) there is a skew element λ in C such that , (c) * is of the first kind, n ≡ 0 or n ≡ 3 (mod 4), and . Examples are given illustrating (c).
DOI : 10.4153/CJM-1991-060-2
Mots-clés : 16A12, 16A28, 16A72 
3rd, W. S. Martindale; Miers, C. Robert. Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution. Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 1045-1054. doi: 10.4153/CJM-1991-060-2
@article{10_4153_CJM_1991_060_2,
     author = {3rd, W. S. Martindale and Miers, C. Robert},
     title = {Nilpotent {Inner} {Derivations} of the {Skew} {Elements} of {Prime} {Rings} {With} {Involution}},
     journal = {Canadian journal of mathematics},
     pages = {1045--1054},
     year = {1991},
     volume = {43},
     number = {5},
     doi = {10.4153/CJM-1991-060-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-060-2/}
}
TY  - JOUR
AU  - 3rd, W. S. Martindale
AU  - Miers, C. Robert
TI  - Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 1045
EP  - 1054
VL  - 43
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-060-2/
DO  - 10.4153/CJM-1991-060-2
ID  - 10_4153_CJM_1991_060_2
ER  - 
%0 Journal Article
%A 3rd, W. S. Martindale
%A Miers, C. Robert
%T Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution
%J Canadian journal of mathematics
%D 1991
%P 1045-1054
%V 43
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-060-2/
%R 10.4153/CJM-1991-060-2
%F 10_4153_CJM_1991_060_2

[1] 1. Herstein, I.N., Sui commutator degli anelli semplici. Rendiconte del Seminario Matematico e Fisico di Milana XXXIII, 1963. Google Scholar

[2] 2. Kovacs, A., Nilpotent derivations. Technion Preprint Series, No. NT-453. Google Scholar

[3] 3. Lanski, C., Differential identities in prime rings with involution, TAMS 292 (1985), 765–787. Google Scholar

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

[5] 5. Martindale, W.S., Lie isomorphisms of prime rings, Trans. Amer. M. Soc. 142 (1969), 437–455. Google Scholar

[6] 6. Martindale, W.S., Lectures at Jilen University. University of Massachusetts, unpublished. Google Scholar

[7] 7. Martindale, W.S. and Miers, C.R., On the iterates of derivations of prime rings, Pac. J. Math. 104 (1983), 179–190. Google Scholar

[8] 8. Martindale, W.S. and Miers, C.R., Herstein s Lie theory revisited, J. Algebra 98 (1986), 14–37. Google Scholar

Cité par Sources :