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Semi-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
E. W. Swokowski
Affiliation:
University of Wisconsin, Milwaukee and Marquette University
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Properties and characterizations for prime and semiprime rings have been provided by A. W. Goldie (2, 3). In a previous paper (1), the authors used the results of (2) to characterize prime and uniform prime modules. It is the aim of the present paper to generalize Goldie's work on semi-prime rings (3) to modules. In this setting certain new properties will appear.

Notationally, in the work to follow, the symbol R always denotes a ring and all R-modules will be right R-modules.

In the theory of rings an ideal C is said to be prime if and only if whenever AB ⊆ C for ideals A and B, then either A ⊆ C or B ⊆ C. A ring is prime if the zero ideal is prime.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 823 - 831
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Feller, E. H. and Swokowski, E. W., Prime modules, Can. J. Math., 17 (1965), 1041–1052.Google Scholar
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