The Gcd Property and Irreducible Quadratic Polynomials
نویسنده
چکیده
The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a PrGfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.
منابع مشابه
Products Of Quadratic Polynomials With Roots Modulo Any Integer
We classify products of three quadratic polynomials, each irreducible over Q, which are solvable modulo m for every integer m > 1 but have no roots over the rational numbers. Polynomials with this property are known as intersective polynomials. We use Hensel’s Lemma and a refined version of Hensel’s Lemma to complete the proof. Mathematics Subject Classification: 11R09
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