Document Type : Original Paper

Author

• M.R. Vedadi

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Islamic Republic of Iran

Abstract

We call a module  essentially retractable if Hom_R for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that Hom_R for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and only if there exists a prime ideal  such that Hom_R. Over semiprime right nonsingular rings, a nonsingular essentially retractable module is precisely a module with non-zero dual. Moreover, over certain rings R, including right FBN rings, it is shown that a nonsingular module M with enough uniforms is essentially retractable if and only if there exist uniform retractable R-modules  and R-homomorphisms  with .

Keywords

• Dual module
• Essentially retractable
• Homo-related