On rings with Engel cycles. II (Q1193226)
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scientific article; zbMATH DE number 62167
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On rings with Engel cycles. II |
scientific article; zbMATH DE number 62167 |
Statements
On rings with Engel cycles. II (English)
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27 September 1992
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The paper is a continuation of part I [see the preceding review Zbl 0786.16014)]. Call \(R\) an \(EC'\)-ring if for each \(x\in R\), there exist distinct positive integers \(n = n(x)\) and \(m = m(x)\) such that \([x,y]_ n = [x,y]_ m\) for all \(y\) in \(R\). \(R\) is an \(E'\)-ring if for each \(x\in R\), \([x,y]_ n = 0\) for all \(y\in R\). They prove that if \(R\) is an \(E'\)- ring then the commutator ideal is nil. If it is an \(EC'\)-ring then the commutator ideal is periodic.
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\(EC'\)-ring
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\(E'\)-ring
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commutator ideal
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0.8560112118721008
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