论文标题
在直接总结中必不可少的模块
Modules in which pure submodule is essential in a direct summand
论文作者
论文摘要
在本文中，我们研究了一个模块类具有直接汇总至关重要的每个纯子模块的属性。这些模块被称为纯扩展模块，这是扩展模块的正确概括。给出了例子和反例。我们研究了纯延伸模块的某些特性，并根据纯延伸模块来表征常规环，半神经环，局部环和PDS环。
In this paper, we study the class of modules have the property that every pure submodule is essential in a direct summand. These modules are termed as pure extending modules which is a proper generalisation of extending modules. Examples and counterexamples are given. We study some properties of pure extending modules and characterize regular ring, semisimple ring, local ring and PDS ring in terms of pure extending modules.
