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Nonsingular retractable modules and their endomorphism rings

Published online by Cambridge University Press:  17 April 2009

Soumaya Makdissi Khuri
Soumaya Makdissi Khuri
Affiliation:
Department of Mathematics, East Carolina University, Greenville, North Carolina 27858, United States of America
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Abstract

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A module RM is said to be retractable if HomR (M, U) ≠ 0 for each nonzero submodule U of M. M is said to be a CS module if every complement submodule of M is a direct summand in M. Retractable modules are compared to nondegenerate modules on the one hand and to e–retractable modules on the other (nondegenerate implies retractable implies e–retractable); and it is shown that if M is nonsingular and retractable, then EndRM is a left CS ring if and only if M is a CS module.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 63 - 71
Copyright
Copyright © Australian Mathematical Society 1991

References

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