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Generalisations of nilpotency of rings

Published online by Cambridge University Press:  20 January 2009

Edmund F. Robertson
Affiliation:
Mathematical Institute, North Haugh, St Andrews
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Extract

In (5) and (6) we studied certain subgroups of infinite dimensional linear groups over rings. In particular we investigated how the structure of the subgroups was related to the structure of the rings over which the linear groups were defined. It became clear that it might prove useful to study generalised nilpotent properties of rings analogous to Baer nilgroups and Gruenberg groups. We look briefly at some classes of generalised nilpotent rings in this paper and obtain a lattice diagram exhibiting all the strict inclusions between the classes.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

(1) Biggs, R. G., A new bound for nil U-rings, Canad. J. Math. 22 (1970), 403407.CrossRefGoogle Scholar
(2) Friedman, P. A., Rings with an idealizer condition, Izv. Vyšs Učebn. Zaved. Mathematika, 15 (1960), 213222 (Russian).Google Scholar
(3) Jacobson, N., Structure of Rings (Amer. Math. Soc. Colloq. Publ. XXXVII).Google Scholar
(4) Kruse, R. L. and Price, D. T., Nilpotent Rings (Gordon and Breach, New York, 1969).Google Scholar
(5) Robertson, E. F., On certain subgroups of GL(R), J. Algebra 15 (1970), 293300.CrossRefGoogle Scholar
(6) Robertson, E. F., Some properties of a subgroup of SpΩ(R), J. London Math. Soc. (2), 4 (1971), 6578.CrossRefGoogle Scholar
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