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Zbl 0765.11045
Geroldinger, A.; Halter-Koch, F.
Non-unique factorizations in block semigroups and arithmetical applications. (English)
[J] Math. Slovaca 42, No.5, 641-661 (1992). ISSN 0139-9918; ISSN 1337-2211/e

The authors apply block semigroups to factorization theory in algebraic number fields. They describe the structure of the set of all blocks which have at most $k$ distinct factorizations into irreducible blocks and apply this to the study of asymptotic behaviour of the counting function of principal ideals of a field $K$ for which the induced block has a given number of factorizations.
[W.Narkiewicz (Wrocław)]

MSC 2000:: *11R27 Units and factorization
11R44 Distribution of prime ideals
20M14 Commutative semigroups

Keywords: block semigroups; factorization; asymptotic behaviour; counting function of principal ideals

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