Malik, Saroj; Mott, Joe L.; Zafrullah, Muhammad The GCD property and irreducible quadratic polynomials. (English) Zbl 0646.13009 Int. J. Math. Math. Sci. 9, 749-752 (1986). 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 Keywords:Prüfer v-multiplication domain; v-operation; Krull domain; Dedekind domain; UFD; PID; Bezout domain; irreducible quadratic polynomial PDFBibTeX XMLCite \textit{S. Malik} et al., Int. J. Math. Math. Sci. 9, 749--752 (1986; Zbl 0646.13009) Full Text: DOI EuDML