The ideal retraction property for idempotent semigroups. (Q877758)
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scientific article; zbMATH DE number 5148908
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The ideal retraction property for idempotent semigroups. |
scientific article; zbMATH DE number 5148908 |
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The ideal retraction property for idempotent semigroups. (English)
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3 May 2007
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A semigroup \(S\) is said to have the `ideal retraction property' provided each of its ideals is the image of an idempotent endomorphism of \(S\). It is proved that a band \(B=[Y;S_\alpha]\) (presented as a semilattice of rectangular bands) has the ideal retraction property if and only if \(B\) is normal and \(Y\) is a tree that contains no \(\omega+1\) chain.
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normal bands
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ideal retractions
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idempotent endomorphisms
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idempotent semigroups
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semilattice homomorphic images
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0.9562944
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0.95163405
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0.94194496
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0.92941844
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0.8892957
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0.8889276
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