Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-14T10:30:53.109Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Albu, T. and Nastasescu, C., Relative finiteness in module theory (Dekker, New York, 1984).Google Scholar
[2]Chatters, A.W. and Khuri, S.M., ‘Endomorphism rings of modules over nonsingular CS rings’, J. London Math. Soc. 21 (1980), 434–444.Google Scholar
[3]Faith, C., Lectures on injective modules and quotient rings 246, Lecture Notes in Mathematics (Springer-Verlag, Heidelberg, Berlin, New York, 1972).Google Scholar
[4]Khuri, S.M., ‘Baer endomorphism rings and closure operators’, Canad. J. Math. 30 (1978), 1070–1078.Google Scholar
[5]Khuri, S.M., ‘Endomorphism rings of nonsingular modules’, Ann. Sci. Math. Quebec 4 (1980), 145–152.Google Scholar
[6]Khuri, S.M., ‘Correspondence theorems for modules and their endomorphism rings’, J. Algebra 122 (1989), 380–396.Google Scholar
[7]Utumi, Y., ‘On rings of which any one-sided quotient ring is two-sided’, Proc. Amer. Math. Soc. 14 (1963), 141–147.Google Scholar