The congruence class of an idempotent in a regular semigroup (Q1174275)
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scientific article; zbMATH DE number 8432
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The congruence class of an idempotent in a regular semigroup |
scientific article; zbMATH DE number 8432 |
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The congruence class of an idempotent in a regular semigroup (English)
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25 June 1992
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Let \(S\) be a regular semigroup and \(\rho\) a congruence on \(S\). For any idempotent \(e\in S\) the class \([e]_ \rho\) is a subsemigroup. G. M. S. Gomes raised the question: is \([e]_ \rho\) necessarily regular? In the paper it is shown that for inverse semigroups and completely regular semigroups the answer is affirmative, but negative for orthodox semigroups.
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congruence
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idempotent
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inverse semigroups
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completely regular semigroups
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orthodox semigroups
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