Schreier domain

An integral domainMathworldPlanetmath D is a pre-Schreier domain if every non-zero element of D is primal. If in addition D is integrally closedMathworldPlanetmath, then D is called a Schreier domain.


  1. 1.

    Every irreducible elementMathworldPlanetmath of a pre-Schreier domain is prime.

  2. 2.

    A gcd domain is a Schreier domain (a proof of this can be found here (

Title Schreier domain
Canonical name SchreierDomain
Date of creation 2013-03-22 14:50:41
Last modified on 2013-03-22 14:50:41
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 13G05
Synonym pre-Schreier
Defines pre-Schreier domain