论文标题
通勤环上的模块的本地自由基
The locally nilradical for modules over commutative rings
论文作者
论文摘要
让$ r $为换向的Unital环，在R中为$ a \。 $aγ_{a}（ - ）$是扭转函数（也称为截面函数）和BAER的下尼尔自由基的概括。建立了函数$aγ_{a}（ - ）$的几种局部全球属性。作为一种应用，获得了有关$ r $ $模型的结果，并推导迄今未知的环理论自由基以及结构定理。
Let $R$ be a commutative unital ring and $a\in R.$ We introduce and study properties of a functor $aΓ_{a}(-),$ called the locally nilradical on the category of $R$-modules. $aΓ_{a}(-)$ is a generalisation of both the torsion functor (also called section functor) and Baer's lower nilradical for modules. Several local-global properties of the functor $aΓ_{a}(-)$ are established. As an application, results about reduced $R$-modules are obtained and hitherto unknown ring theoretic radicals as well as structural theorems are deduced.
