Partial actions and cyclic kummer’s theory

Abstract

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 Borevich. In particular, we provide necessary and sufficient conditions to determine when a partial [Formula: see text]-Kummerian extension is equivalent to either a radical or an [Formula: see text]-radical extension, for some subgroup [Formula: see text] of the cyclic group [Formula: see text].