Ivan Shishkin, Rye (1878)

Problems/General algebraExerciseUnreviewed

Unicité de l’élément neutre

by Ancient Tree·translated by Catalpa·
14
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This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

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These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit (M,∗)(M,*) un magma unifère doté de élément neutre ee. Montrez que ee est unique.

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Solution by Ancient Tree · translated by Catalpa

Discussions0 useful votes

On suppose que e′e' est un autre élément neutre. En particulier, cela signifie que, pour x:=ex:=e:
e∗e′=x∗e′=x=e.e*e'=x*e'=x=e .Mais comme ee est un élément neutre, par définition, pour y:=e′y:=e':
e∗e′=e∗y=y=e′.e*e'=e*y=y=e'.Donc on peut conclure que e=e′e=e'.

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