When is a power series ring n-root closed? Original Research Article

Given commutative rings A subset of or equal to B, we present a necessary and sufficient condition for the power series ring A[[X]] to be n-root closed in B[[X]]. This result leads to a criterion for the the power series ring A[[X]] over an integral domain A to be n-root closed (in its quotient field). For a domain A, we prove: if A is Mori (for example, Noetherian), then A[[X]] is n-root closed iff A is n-root closed; if A is Prüfer, then A[[X]] is root closed iff A is completely integrally closed.