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Cet article traite de certains préordres généralisant le bon ordre. On étudie les rapports entre la notion de préordre artinien d’incomparabilité finie (pour qui toute partie a des éléments minimaux incomparables en nombre fini) et deux notions de prémeilleur ordre introduites successivement par Hash-Williams en 1965 puis par Jullien en 1969. On montre que ces deux notions sont identiques...
Cameron introduced the orbit algebra of a permutation group and conjectured that this algebra is an integral domain if and only if the group has no finite orbit. We prove that this conjecture holds and in fact that the age algebra of a relational structure is an integral domain if and only if is age-inexhaustible. We deduce these results from a combinatorial lemma asserting that if a product of two non-zero elements of a set algebra is zero then there is a finite common tranversal of their supports....
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