  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
$C_n$.

Rings and Algebras