Relatively polyform modules.

In this paper, we investigate polyform modules and introduce the notion of relatively polyform modules over a ring R. Some new characterizations and properties of polyform modules are obtained. For a retractable polyform module M R , it is proved that the maximal right ring of quotients of End R (M) is End R (E ̃ (M)) , where E ̃ (M) is the rational hull of M. Moreover, we characterize nonsingular modules by using the relatively polyform property. In addition, it is proved that the class of all polyform right R -modules is closed under submodules and rational extensions. [ABSTRACT FROM AUTHOR]