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单词 SchreierDomain
释义

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.

Remarks.

  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 (http://planetmath.org/ProofThatAGcdDomainIsIntegrallyClosed)).

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更新时间:2025/5/4 21:10:56