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Schreier domain (Definition)

An integral domain $ D$ is a pre-Shreier 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. Every irreducible element of a pre-Schreier domain is prime.
  2. A gcd domain is a Schreier domain.



"Schreier domain" is owned by CWoo.
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Also defines:  pre-Schreier domain
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Cross-references: gcd domain, prime, irreducible element, integrally closed, addition, primal, integral domain
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This is version 1 of Schreier domain, born on 2004-11-22.
Object id is 6514, canonical name is SchreierDomain.
Accessed 1508 times total.

Classification:
AMS MSC: 13G05 (Commutative rings and algebras :: Integral domains)
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