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Prime Modules

Published online by Cambridge University Press:  20 November 2018

E. H. Feller  and
E. W. Swokowski
E. H. Feller
Affiliation:
University of Wisconsin-Milwaukee and Marquette University
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Characterizations for prime and semi-prime rings satisfying the right quotient conditions (see § 1) have been determined by A. W. Goldie in (4 and 5). A ring R is prime if and only if the right annihilator of every non-zero right ideal is zero. A natural generalization leads one to consider right R-modules having the properties that the annihilator in R of every non-zero submodule is zero and regular elements in R annihilate no non-zero elements of the module. This is the motivation for the definition of prime module in § 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 1041 - 1052
Copyright
Copyright © Canadian Mathematical Society 1965

References

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