Geodesic
A New Bound for Nil U-Rings
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 403-407

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

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) I λ is an ideal of I λ+1 for all λ < β;(2) If α is a limit ordinal number, then Iα = ∪λ<α Iλ.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. 
Biggs, R. G. A New Bound for Nil U-Rings. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 403-407. doi: 10.4153/CJM-1970-049-0
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[1] 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] 2. Divinsky, N. J., Rings and radicals (Univ. Toronto Press, Toronto, Ontario, 1965). Google Scholar

[3] 3. Freïdman, P.A., Rings with an idealizer condition. I, Izv. Vyss. Ucebn. Zaved. Matematika 1960, no. 2 (15), 213–222. (Russian) Google Scholar

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