English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper is inspired by Michael Artin's paper "On The Join of HenselRings". In his paper, Artin proves that in an absolutely integrally closed ringthe sum of two prime ideals is either prime or the whole ring. A moreelementary proof of the previous statement is given in M. Hochster and C.Huneke's "Infinite Integral Extensions and Big Cohen-Macaulay Algebras" for thelarger class of quadratically closed rings. Motivated by Hochster and Huneke'sproof, we give an elementary proof of the fact that an absolutely integrallyclosed ring has no polygons. We prove this for the larger class of 2n-adicallyclosed rings, after defining n-adically closed rings. The notion of irreducibleintersection property is introduced, and a necessary and sufficient conditionis proved for a ring to have this property. Other ring and scheme theoreticproperties of absolutely integrally closed rings and n-adically closed ringsare shown in detail.

Polygons in Quadratically Closed Rings and Properties of n-adically Closed Rings