F-纯子模

F-pure Submodules

设F是环R上的右Gabriel拓扑,文中用线性方程组给出了S-R-模N是S-R-模M的F-纯子模的充分必要条件,并对绝对F-纯模进行了刻划。

Let R be a ring with identity and F a right Gabriel topology on R.The necessary and sufficient condition that a S-R-moduleN is a F-pure submodule of S-R-module M is giv- en in terms of system of linear equations over N/t(N),where t is left exact redical corre- sponding to F.Also,absolutely F-pure modules are characterized.