Waterhouse, William C. Quadratic polynomials and unique factorization. (English) Zbl 1036.13004 Am. Math. Mon. 109, No. 1, 70-72 (2002). From the paper: Let \(A\) be an integral domain. Suppose that every quadratic polynomial in \(A[X]\) having roots in the fraction field of \(A\) is a product of first-degree factors in \(A[X]\). Then every irreducible element in \(A\) is prime. Cited in 1 ReviewCited in 3 Documents MSC: 13A05 Divisibility and factorizations in commutative rings 13G05 Integral domains 13F20 Polynomial rings and ideals; rings of integer-valued polynomials Keywords:irreducible element; prime element; factorization of quadric polynomials PDFBibTeX XMLCite \textit{W. C. Waterhouse}, Am. Math. Mon. 109, No. 1, 70--72 (2002; Zbl 1036.13004) Full Text: DOI