论文标题
部分动作和循环库默的理论
Partial actions and cyclic Kummer's theory
论文作者
论文摘要
我们介绍了有限群体部分galois扩展的通勤环的环状kummer扩展理论，扩展了A. Z. Borevich开发的交换环的Kummer扩展理论的一些众所周知的结果。特别是，我们提供了必要的条件，以确定何时部分$ n $ n $ -kummerian扩展名等同于激进或$ i $ - 激进的扩展，对于某些循环组$ c_n $的亚组$ i $。
We introduce a theory of cyclic Kummer extensions of commutative rings for partial Galois extensions of finite groups, extending some of the well-known results of the theory of Kummer extensions of commutative rings developed by A. Z. Borevich. In particular, we provide necessary and sufficient conditions to determine when a partial $n$-kummerian extension is equivalent to either a radical or a $I$-radical extension, for some subgroup $I$ of the cyclic group $C_n$.
