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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 |

### References:

[1] | Carruth, J.H., Hildebrant, J.A., and Koch, R.J.: The Theory of Topological Semigroups I. Pure and Applied Mathematics series, Marcel Dekker, Inc., New York, 1983. · Zbl 0515.22003 |

[2] | Clifford, A.H., and Preston, G.B.: The Algebraic Theory of Semigroups I. Math. Surveys, 7, Amer. Math. Soc., 1961. · Zbl 0111.03403 |

[3] | Tamura, T.: The theory of construction of finite semigroups III. Osaka Math J. 10, 191-204. · Zbl 0084.02604 |

[4] | Yamada, M.: Construction of finite commutative z-semigroups. Proc, Japan Acad. 40, 94-98. · Zbl 0121.26903 · doi:10.3792/pja/1195522841 |

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