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Lower Radicals in Associative Rings

Published online by Cambridge University Press:  20 November 2018

J. F. Watters
J. F. Watters*
Affiliation:
The University, Leicester, England
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Given a homomorphically closed class of (not necessarily associative) rings , the lower radical property determined by is the least radical property for which all rings in are radical. Recently (7) a process of constructing the lower radical property from a class of associative rings has been given which terminates after a countable number of steps. In this process, an ascending chain of classes

is obtained and the property of being a ring in the class is the lower radical property determined by . In Theorem 1 we give another characterization of the rings in the class , λ ∈ {1, 2, …, omega;0}, and a procedure for constructing the lower radical determined by in an arbitrary associative ring is given.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 466 - 476
Copyright
Copyright © Canadian Mathematical Society 1969

References

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