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Non-unique factorizations in block semigroups and arithmetical applications. (English) Zbl 0765.11045
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.

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