Chiang Mai Journal of Science

Let  R be a commutative ring with non-zero identity. We define a proper submodule Nof an  R -module M to be quasi-primary if  rad(N :_RM) = P is a prime ideal of  R. In this case we also say that N is a P-quasi-primary submodule of M. A number of results concerning quasi-primary submodules are given. For example, we show that over a Prüfer domain of finite character  R , every non-zero R-submodule of a module M is the intersection of  finite number of  quasi-primary submodules with incomparable radicals.