# Schreier domain

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

Remarks.

1. 1.

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

2. 2.

A gcd domain is a Schreier domain (a proof of this can be found here (http://planetmath.org/ProofThatAGcdDomainIsIntegrallyClosed)).

Title Schreier domain SchreierDomain 2013-03-22 14:50:41 2013-03-22 14:50:41 CWoo (3771) CWoo (3771) 7 CWoo (3771) Definition msc 13G05 pre-Schreier pre-Schreier domain