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Algèbres Commutatives Engendrées Par Leurs Éléments Idempotents

Published online by Cambridge University Press:  20 November 2018

Klaus Keimel
Klaus Keimel*
Affiliation:
Collège Scientifique Universitaire de Tours, Tours, France
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Dans ce travail, R désignera toujours un anneau commuta tif ayant un élément unité 1. Les R-algèbres considérées seront supposées associatives. Si A est une R-algèbre, nous supposerons toujours 1 · a = a quel que soit a ∊ A. Si B ⊂ A, nous désignerons par Ann(B) l'ensemble des r ∊ R tels que rB = {0}.

Soit A une R-algèbre commutative (avec ou sans élément unité). Nous désignerons par EA l'ensemble des éléments idempotents de A. Si l'on définit pour e, f ∊ EA,

alors EA devient un treillis distributif relativement complémenté dont 0 est le plus petit élément [2].

Nous nous intéresserons aux R-algèbre commutatives engendrées par leurs éléments idempotents.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 1071 - 1078
Copyright
Copyright © Canadian Mathematical Society 1970

References

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