论文标题
关于基本模块的几个评论
Few remarks on essential modules
论文作者
论文摘要
在本文中，对某些子模块的适当基本扩展的整体域和主要理想域的模块进行了分类。我们介绍了一个新的模块类别，我们称为$ \ mathrm {sm} $模块，并证明Artinian模块，本地有限的模块和有限长度的模块都是SM模块的适当子类。我们还表明，非偏见$ \ mathrm {sm} $模块具有必不可少的socles。此外，我们表明，与非无空扭转部分的整体域上的非隔离模块不具备基本的SOCLES。
In the present paper, modules over integral domains and principal ideal domains that are proper essential extensions of some submodules are classified. We introduce a new class of modules that we call $\mathrm{SM}$ modules and show that the class of Artinian modules, locally finite modules, and modules of finite lengths are all proper subclasses of SM modules. We also show that non-semisimple $\mathrm{SM}$ modules possess essential socles. Further, we show that non-semieimple modules over integral domains with nonempty torsion-free parts do not possess essential socles.
