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Passman-Zalesskii Radical of group algebras

Published online by Cambridge University Press:  20 January 2009

I. Sinha
I. Sinha
Affiliation:
Michigan State University, East Lansing, Michigan 48823
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Recently Passman (attributing the origin of the idea to Zalesskii) has defined the following ideal in a ring, (2).

Definition. For a unitary ring R,

N * R = {α ∈ R | αS is nilpotent for all finitely generated subrings S of R}.

For a group algebra KG over a field K of characteristic p ≠ 0, he has proved the radical property:

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 1 , March 1974 , pp. 71 - 72
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Passman, D. S., Infinite Group-Rings (Marcel Dekker Inc., New York, 1971).Google Scholar
(2) Passman, D. S., A New Radical for Group-Rings (to appear).Google Scholar
(3) Sinha, I., Augmentation-maps of Subgroups of a group, Math. Z. 94 (1966), 193–206.CrossRefGoogle Scholar
(4) Wallace, D. A. R., Some Applications of Subnormality in groups in the study of Group-Algebras, Math. Z. 108 (1968), 53–62.CrossRefGoogle Scholar