The primitive element theorem for commutative algebras (Q2716461)
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scientific article; zbMATH DE number 1599019
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The primitive element theorem for commutative algebras |
scientific article; zbMATH DE number 1599019 |
Statements
29 November 2002
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primitive element
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algebraic ring extension
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integrally closed integral domain
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Prüfer domain
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The primitive element theorem for commutative algebras (English)
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An extension \(R\subset T\) of commutative rings has FIP if the set of \(R\)-subalgebras of \(T\) is finite. In this case \(T\) must be algebraic over \(R\) but in general \(T\) is not generated as an \(R\)-algebra by one element as it happens in the field case. If \(R\subset T\) is an integral extension which has FIP then \(T\) is a module finite \(R\)-algebra. If \(K\) is a field, one obtain a complete description of those extensions \(K\subset T\) having FIP.
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