Schreier domain
An integral domain is a pre-Schreier domain if every non-zero element of is primal. If in addition is integrally closed
, then is called a Schreier domain.
Remarks.
- 1.
Every irreducible element
of a pre-Schreier domain is prime.
- 2.
A gcd domain is a Schreier domain (a proof of this can be found here (http://planetmath.org/ProofThatAGcdDomainIsIntegrallyClosed)).