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Si introduce un'estensione della nozione d'equivalenza di Green, e di essa si studiano varie proprietà. L'applicazione al caso particolare del semi-gruppo degli endomorfismi di un'algebra astratta (nel senso di G. Birkhoff) , fa apparire l'interesse di considerare questo semi-gruppo come un sotto-semi-gruppo del semi-gruppo delle applicazioni di in ; e ciò permette di caratterizzare i gruppi di Schutzenberger associati ad alcune classi di equivalenza.
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