On the structure of rings which are sums of two subrings. (Q1764455)
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scientific article; zbMATH DE number 2138534
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the structure of rings which are sums of two subrings. |
scientific article; zbMATH DE number 2138534 |
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On the structure of rings which are sums of two subrings. (English)
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25 February 2005
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The paper is addressed to the following problem: Let \(R=R_1+R_2\) be a ring, where \(R_1\) is a nil ring and \(R_2\) is a reduced ring. Whether in this situation \(R_1\) is an ideal? The authors show that it is indeed in some particular cases, e.g., \(R_1\) is locally nilpotent and \(R_2\) has finite Goldie dimension, or \(R_1\) is a prime radical ring and \(R_2\) is a domain.
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nil rings
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reduced rings
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prime radical
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sums of two rings
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semidirect sums
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