Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-31T19:23:52.098Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Information

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

Bibliographie

1. Daims, J. and Hofmann, K. H., Representation of rings by sections, Mem. Amer. Math. Soc, No. 83 (Amer. Math. Soc, Providence, R.I., 1968).Google Scholar
2. Foster, A. L., The idempotent elements of a commutative ring form a Boolean algebra; ringduality and transformation theory, Duke Math. J. 12 (1945), 143–152.Google Scholar
3. Foster, A. L., p-rings and their Boolean vector representation, Acta Math. 84 (1951), 231–261.Google Scholar
4. Keimel, K., Darstellung von Halbgruppen und universellen Algebren durch Schnitte in Garben; bireguldre Halbgruppen, Math. Nachr. 45 (1970), 81–96.Google Scholar
5. McCoy, N. H. and Montgomery, D., A representation of generalized Boolean rings, Duke Math. J. 3 (1937), 455–459.Google Scholar
6. Ph., Nanzetta, A representation theorem for relatively complemented distributive lattices, Can. J. Math. 20 (1968), 756–758.Google Scholar
7. Pierce, R. S., Modules over commutative regular rings, Mem. Amer. Math. Soc, No. 70 (Amer. Math. Soc, Providence, R.I., 1967).Google Scholar
8. Stone, M. H., Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375–481.Google Scholar
9. Subramanian, H., Integer-valued continuous functions, Bull. Soc. Math. France 97 (1969), 275–283.Google Scholar
10. Zemmer, J. L., Some remarks on p-rings and their Boolean geometry, Pacific J. Math. 6 (1956), 193–208.Google Scholar