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scientific article; zbMATH DE number 6052220
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regular pullbacks |
scientific article; zbMATH DE number 6052220 |
Statements
21 April 2016
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2 July 2012
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pullback
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conductor square
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coherent-like properties
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atomic domains
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coherent rings
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Noetherian rings
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Prüfer rings
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pullbacks
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0.84068394
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0.83984524
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0.8373677
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0.8369404
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Regular pullbacks (English)
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Let \(\varphi : T \longrightarrow B\) be a surjective homomorphism of commutative rings with identity, \(C =\) ker\(\varphi\), and \(A\) a subring of \(B\). The pullback \(R = \varphi^{-1}(A)\) is called a regular pullback if the common ideal \(C\) contains a \(T\)-regular element. In this paper, the authors both survey old results and give some new results about pullbacks. These relate to the transfer of ring-theoretic properties such the Noetherian property, Prüfer conditions, coherence, the \(n\)-generator property, and factorization. The new results focus on regular pullbacks.NEWLINENEWLINEFor the entire collection see [Zbl 1237.13006].
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