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)).
| 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 |