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The Jacobson Radical and Regular Modules

Published online by Cambridge University Press:  20 November 2018

David J. Fieldhouse
David J. Fieldhouse*
Affiliation:
University of Guelph
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Let A be an associative, but not necessarily commutative, ring with identity, and J = J(A) its Jacobson radical. A (unital) module is regular iff every submodule is pure (see (1)). The regular socle R(M) of a module M is the sum of all its submodules which are regular. These concepts have been introduced and studied in (2).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 141
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Cohn, P. M., On the free product of associative rings, I, Math. Z. 71 (1959) 380-398.Google Scholar
2. Fieldhouse, D., Pure Theories, Math. Annalen 184 (1969) 1-18.Google Scholar