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ABSTRACT
A module M is called (strongly) FI-extending if every fully invariant submodule is essential in a (fully invariant) direct summand. The class of strongly FI-extending modules is properly contained in the class of FI-extending modules and includes all nonsingular FI-extending (hence nonsingular extending) modules and all semiprime FI-exten ding rings. In this paper we examine the behavior of the class of strongly FI-extending modules with respect to the preservation of this property in submodules, direct summands, direct sums, and endomorphism rings.
ACKNOWLEDGMENTS
The authors are grateful for the thorough reading of the manuscript and suggestions by the referee. Furthermore we appreciate the comments by R. Wisbauer which enabled us to generalize many of our results for nonsingular modules to non-M-singular modules. The first author appreciates the gracious hospitality received at Ohio State University at Lima and at Busan National University. The second author was partially supported by Korea Research Foundation, Research Grant Project No.DP0004 in 2000–2001. The third author wishes to acknowledge partial support received from an OSU-Lima research grant and a grant from Mathematics Research Institute, Columbus.