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A New Bound for Nil U-Rings

Published online by Cambridge University Press:  20 November 2018

R. G. Biggs
R. G. Biggs*
Affiliation:
The University of Western Ontario, London, Ontario
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A U-ring is a ring in which every subring is a meta ideal. A meta ideal of a ring R is a subring I of R which lies in a chain of subrings,

with the properties:

(1) Iλ is an ideal of Iλ+1 for all λ < β;

(2) If α is a limit ordinal number, then Iα = ∪λ<αIλ.

Freidman [3] proved that every nil U-ring is a locally nilpotent ring. Since there are many locally nilpotent rings which are not U-rings, the class of locally nilpotent rings is not a very good bound for the class of nil U-rings. This paper establishes a new bound for nil U-rings based on a property of the multiplicative semigroup of the ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 2 , 01 April 1970 , pp. 403 - 407
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Baer, R., Meta ideals, Report of a conference on linear algebras, June, 1956, pp. 33–52 (National Academy of Sciences-National Research Council, Washington, Publ., 1957).Google Scholar
2. Divinsky, N. J., Rings and radicals (Univ. Toronto Press, Toronto, Ontario, 1965).Google Scholar
3. Freïdman, P.A., Rings with an idealizer condition. I, Izv. Vyss. Ucebn. Zaved. Matematika 1960, no. 2 (15), 213–222. (Russian)Google Scholar