The endomorphism structure of simple faithful \(S\)-acts (Q1300592)
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scientific article; zbMATH DE number 1330707
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The endomorphism structure of simple faithful \(S\)-acts |
scientific article; zbMATH DE number 1330707 |
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The endomorphism structure of simple faithful \(S\)-acts (English)
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8 December 1999
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Let \(S\) be a semigroup and \(M\) a left \(S\)-act. The author proves the following: Let \(M\) be a simple faithful \(S\)-act. Then the following are equivalent: 1. \(\text{End }M\) is transitive. 2. \(S\) is commutative. 3. \(\text{End }M\cong S\cong Z_p\), where \(Z_p\) denotes a cyclic group of prime order. Then we also have \(S\cong M\) as \(S\)-acts. This is a result which had already been proved by R.~Oehmke with different methods.
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semigroups
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left acts
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simple acts
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faithful acts
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primitive acts
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endomorphisms
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