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L'enveloppe de Translations d'un Demi-Treillis de Groupes

  • Mario Petrich (a1)

Extract

L'enveloppe de translations d'un demi-groupe présente un intérêt particulier pour les deux raisons suivantes : d'une part, elle apparaît d'une façon naturelle dans la construction des extensions idéales des demi-groupes, et d'autre part, elle est souvent utilisée pour des caractérisations abstraites des demi-groupes. Afin de l'appliquer aux problèmes particuliers, il est important de fournir des constructions qui, pour un demi-groupe donné sous une forme ou une autre, soient aussi explicites que possible. Un exemple d'une telle construction est celle de l'enveloppe de translations d'un demi-groupe de matrices de Rees (voir [4]) et ses nombreuses applications [5 ; 6 ; 7 ; 8].

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References

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1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups. Vol.I (Amer. Math. Soc, Providence, 1961).
2. Gluskin, L. N., Les idéaux des demi-groupes(en russe), Mat. Sb. 55 (1961), 421448.
3. Grillet, P. A. and Petrich, M., Ideal extensions of semigroups, Pacific J. Math. 26 (1968), 493508.
4. Petrich, Mario, The translational hull of a completely 0-simple semigroup, Glasgow Math. J. 9 (1968), 111.
5. Petrich, Mario, Translational hull and semigroups of binary relations, Glasgow Math. J. 9 (1968), 1221.
6. Petrich, Mario, The semigroup of endomorphisms of a linear manifold, Duke Math. J. 86 (1969), 145152.
7. Petrich, Mario, Representations of semigroups and the translational hull of a regular Rees matrix semigroup, Trans. Amer. Math. Soc. 143 (1969), 303318.
8. Petrich, Mario, Certain dense embeddings of regular semigroups, Trans. Amer. Math. Soc. 155 (1971), 333343.
9. Petrich, Mario, On ideals of a semilattice, Czechoslovak Math. J. 22 (1972), 361367.
10. Ponizovski, I. S., Une remarquesur les demi-groupes inverses (en russe), Uspehi Mat. Nauk 20 (1965), 147148.
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L'enveloppe de Translations d'un Demi-Treillis de Groupes

  • Mario Petrich (a1)

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