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IV.—On the Radicals of Rings of Row-finite Matrices*

Published online by Cambridge University Press:  14 February 2012

E. M. Patterson
E. M. Patterson
Affiliation:
King's College, Aberdeen.
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Synopsis

Let R be a ring and let ΓR be the Jacobson-Perlis radical. It is shown that the radical of the ring of row-finite matrices over R is the ring of row-finite matrices over ΓR if and only if ΓR is right-vanishing. This is done by extending the results of an earlier paper. One interesting consequence of the theorem is noted.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 66 , Issue 1 , 1962 , pp. 42 - 46
Copyright
Copyright © Royal Society of Edinburgh 1962

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References

References to Literature

Jacobson, N., 1956. “Structure of Rings”, Amer. Math. Soc. Colloq. Publ., 37.CrossRefGoogle Scholar
Levitzki, J., 1954. “Contributions to the Theory of Nil Rings”, Riveon Lemat., 7, 50–70.Google Scholar
Patterson, E. M., 1961. “On the Radicals of Certain Rings of Infinite Matrices”, Proc. Roy. Soc. Edin. A, 65, 263–271.Google Scholar