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The GCD property and irreducible quadratic polynomials. (English) Zbl 0646.13009

Summary: The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer 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.
Reviewer: M.E.Keating

MSC:

13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13A15 Ideals and multiplicative ideal theory in commutative rings
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