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Rings with Central Idempotent or Nilpotent Elements

Published online by Cambridge University Press:  20 January 2009

M. P. Drazin
M. P. Drazin
Affiliation:
Department of Mathematics, North Western University, Evanston, Illinois, U.S.A.
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It is easy to see (cf. Theorem 1 below) that the centrality of all the nilpotent elements of a given associative ring implies the centrality of every idempotent element; and (Theorem 7) these two properties are in fact equivalent in any regular ring. We establish in this note various conditions, some necessary and some sufficient, for the centrality of nilpotent or idempotent elements in the wider class of π-regular rings (in Theorems 1, 2, 3 and 4 the rings in question are not even required to be π-regular).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 4 , May 1958 , pp. 157 - 165
Copyright
Copyright © Edinburgh Mathematical Society 1958

References

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