On Purely –Extending Modules - Al-Bahrani, B. (Iraqi Journal of Science, 2023)
In this note we consider a generalization of the notion of a purely extendingmodules, defined using y– closed submodules.We show that a ring R is purely y – extending if and only if every cyclic nonsingularR – module is flat. In particular every nonsingular purely y extending ring isprincipal flat.