Semigroups containing no maximal ideals (Q1825968)
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scientific article; zbMATH DE number 4122239
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semigroups containing no maximal ideals |
scientific article; zbMATH DE number 4122239 |
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Semigroups containing no maximal ideals (English)
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1990
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A two-sided ideal \(M\) of a semigroup \(S\) is said to be covered if \(M\subseteq S(S\setminus M)S\). The author proves that a semigroup has no maximal ideals iff each of its principal ideals is covered. If a semigroup has no greatest ideal and the set of its principal ideals is up-directed then it has no maximal ideals. Similar results hold for maximal one-sided ideals.
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covered ideals
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maximal ideals
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principal ideals
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