On Rings with Involution
Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 794-799
Voir la notice de l'article provenant de la source Cambridge University Press
In this note we prove some results which assert that under certain conditions the involution on a prime ring must satisfy a form of positive definiteness. As a consequence of the first of our theorems we obtain a fairly short and simple proof of a recent theorem of Lanski [3]. In fact, in doing so we actually generalize his result in that we need not avoid the presence of 2-torsion. One can easily adapt Lanski's original proof, also, to cover the case in which 2-torsion is present. This result of Lanski has been greatly generalized in a joint work by Susan Montgomery and ourselves [2].
Herstein, I. N. On Rings with Involution. Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 794-799. doi: 10.4153/CJM-1974-074-5
@article{10_4153_CJM_1974_074_5,
author = {Herstein, I. N.},
title = {On {Rings} with {Involution}},
journal = {Canadian journal of mathematics},
pages = {794--799},
year = {1974},
volume = {26},
number = {4},
doi = {10.4153/CJM-1974-074-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-074-5/}
}
[1] 1. Herstein, I. N., Topics in ring theory (Univ. of Chicago Press, Chicago, 1969). Google Scholar
[2] 2. Herstein, I. N. and Susan Montgomery, Invertible and regular elements in rings with involution, J. Algebra 25 (1973), 390–400. Google Scholar
[3] 3. Lanski, Charles, Rings with involution whose symmetric elements are regular, Proc. Amer. Math. Soc. 83 (1972), 264–270. Google Scholar
[4] 4. Lanski, Charles and Montgomery, S., Lie structure of prime rings of characteristic 2 (to appear). Google Scholar
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