The GCD property and irreducible quadratic polynomials (Q1103676)
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scientific article; zbMATH DE number 4053765
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The GCD property and irreducible quadratic polynomials |
scientific article; zbMATH DE number 4053765 |
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The GCD property and irreducible quadratic polynomials (English)
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1986
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Summary: The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.
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Prüfer v-multiplication domain
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v-operation
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Krull domain
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Dedekind domain
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UFD
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PID
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Bezout domain
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irreducible quadratic polynomial
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