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On \(m\)-semigroups. (English) Zbl 0901.20046

The paper concerns semigroups \(S\) in which every subsemigroup \(T\) is contained in an ideal \(J\) of \(S\) in such a way that \(T\) is an ideal of \(J\). If this is true, then one can put \(J=S^1TS^1\). Semigroups with this property are closed under subsemigroups and homomorphic images, contain exactly one idempotent, which is zero, and are of index \(\leq 5\). If they are commutative, then they are Archimedean. Similar results are also proved for topological semigroups \(S\), where every closed subsemigroup \(T\) appears as a closed ideal of some closed ideal \(J\) of \(S\).
Reviewer: A.Drápal (Praha)

MSC:

20M10 General structure theory for semigroups
20M12 Ideal theory for semigroups
22A15 Structure of topological semigroups
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References:

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