When is a power series ring n-root closed?

David F. Anderson, David E. Dobbs, Moshe Roitman

Research output: Contribution to journalArticlepeer-review


Given commutative rings A ⊆ 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.

Original languageEnglish
Pages (from-to)111-131
Number of pages21
JournalJournal of Pure and Applied Algebra
Issue number2
StatePublished - 13 Jan 1997

ASJC Scopus subject areas

  • Algebra and Number Theory


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