On algebraic number fields with non-unique factorization. II. (English) Zbl 0148.27801

Summary: The author [Colloq. Math. 27, 275–276 (1973; Zbl 0263.12004)] has proved that in an algebraic number field with class number \(h > 1\), almost all integers have non-unique factorization into irreducible factors, and if the field is normal then almost all rational integers have non-unique factorization. The reviewer [Proc. Am. Math. Soc. 11, 391–392 (1960; Zbl 0202.33101)] proved that in fields with class number \(>2\), there are integers which have factorizations into irreducible factors with different lengths. The author showed, in the paper cited, that almost all integers have this property and that in the case of quadratic fields almost all rational integers have this property. In the present paper he proves this result for all normal extensions of the rationals with class number.


11R27 Units and factorization
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