When is a power series ring n-root closed?

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

doi:10.1016/0022-4049(95)00167-0

When is a power series ring n-root closed?

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	111-131
Number of pages	21
Journal	Journal of Pure and Applied Algebra
Volume	114
Issue number	2
DOIs	https://doi.org/10.1016/0022-4049(95)00167-0
State	Published - 13 Jan 1997

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-4049(95)00167-0

Cite this

@article{a8c6635911bd4803a76c697e3629ac90,

title = "When is a power series ring n-root closed?",

abstract = "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 Pr{\"u}fer, then A[[X]] is root closed iff A is completely integrally closed.",

author = "Anderson, {David F.} and Dobbs, {David E.} and Moshe Roitman",

year = "1997",

month = jan,

day = "13",

doi = "10.1016/0022-4049(95)00167-0",

language = "English",

volume = "114",

pages = "111--131",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",