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A Note on Lower Radical Constructions for Associative Rings

Published online by Cambridge University Press:  20 November 2018

A.G. Heinicke
A.G. Heinicke*
Affiliation:
University of British Columbia
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In [2], a construction for the lower radical class R∘ (η) with respect to a class η of rings was given as the union of an inductively defined ascending transfinite chain of classes of rings. It was shown there that this construction terminates, for associative rings, at ω∘, the first infinite ordinal, in the sense that if {ηα: α an ordinal} is the chain, then R∘ (η) =ηω∘. Also, examples of classes η for which R∘ (η) = η1, η2, η3 were given.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 23 - 30
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Divinsky, N., Rings and Radicals. Toronto: University of Toronto Press, 1965.Google Scholar
2. Sulinski, A., Anderson, R. and Divinsky, N., Lower radical properties for associative and alternative rings. J. Lond. Math. Soc., 41 (1966), 417-424.10.1112/jlms/s1-41.1.417Google Scholar
3. Zariski, O. and Samuel, P., Commutative algebra I. Princeton: D. Van Nostrand Company, Inc., 1958.Google Scholar