ABSTRACT
A module M is said to be square free if whenever its submodule is isomorphic to N2 = N⊕N for some module N, then N = 0. Dually, a module M is said to be d-square free (dual square free) if whenever its factor module is isomorphic to N2 for some module N, then N = 0. In this paper, we give some fundamental properties of d-square free modules and study rings whose d-square free modules are closed under submodules or essential extensions.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to thank Professors Kazutoshi Koike and Pedro A. Guil Asensio for valuable comments. The authors are also grateful to the referee for careful reading and nice comments.