On dual of square free modules

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.

KEYWORDS:

• Dual square free module
• H-supplemented module
• perfect ring

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16D40
• Secondary 16D70

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.