论文标题
偏斜多项式环上的关键和注射模块
Critical and injective modules over skew polynomial rings
论文作者
论文摘要
让$ r $为Krull Dimension One的可交换本地$ K $ -K $ - $ K $是一个字段。令$α$为$ r $的$ k $ -algebra自动形态，并将$ s $定义为偏斜的多项式代数$ r [θ; α] $。我们提供的，根据$ r $的一些其他假设，是$ s $的标准，以使所有简单的$ s $ modules当地的注射式船体在本地Artinian-也就是说，对于$ s $来满足属性$（\ diamond）$。众所周知，如果$α$是有限的订单，则$ s $具有此属性，但是为了在$α$具有无限订单时获得标准，我们发现在这种情况下，有必要对所有环环（krull）关键$ s $ mmodules进行分类，这一结果可能是独立的。在上述的帮助下，我们证明$ \ hat {s} = k [[x]] [θ，α] $满足所有$ k $ -k $ -algebra automorthisms $α$ a $ k [[x] $的$（\ diamond）$。
Let $R$ be a commutative local $k$-algebra of Krull dimension one, where $k$ is a field. Let $α$ be a $k$-algebra automorphism of $R$, and define $S$ to be the skew polynomial algebra $R[θ; α]$. We offer, under some additional assumptions on $R$, a criterion for $S$ to have injective hulls of all simple $S$-modules locally Artinian - that is, for $S$ to satisfy property $(\diamond)$. It is easy and well known that if $α$ is of finite order, then $S$ has this property, but in order to get the criterion when $α$ has infinite order we found it necessary to classify all cyclic (Krull) critical $S$-modules in this case, a result which may be of independent interest. With the help of the above we show that $\hat{S}=k[[X]][θ, α]$ satisfies $(\diamond)$ for all $k$-algebra automorphisms $α$ of $k[[X]]$.
