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Quadratic polynomials and unique factorization. (English) Zbl 1036.13004

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.

MSC:

13A05 Divisibility and factorizations in commutative rings
13G05 Integral domains
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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