Arithmetical semigroups defined by congruences (Q810642)
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scientific article; zbMATH DE number 4214262
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Arithmetical semigroups defined by congruences |
scientific article; zbMATH DE number 4214262 |
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Arithmetical semigroups defined by congruences (English)
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1991
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The paper investigates the arithmetic of multiplicative subsemigroups of natural numbers defined by congruences using divisor theoretic methods. Necessary and sufficient conditions for the existence of a divisor theory and for unique factorization are given. As a corollary a new and simpler proof of the well-known theorem characterizing arithmetical congruence semigroups with unique factorization is obtained.
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multiplicative subsemigroups of natural numbers
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congruences
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divisor theory
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unique factorization
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arithmetical congruence semigroups
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