In this note we will prove that if is a local domain such that its formal fibers are geometrically normal, then the number of minimal prime ideals in the -adic completion equals exactly the number of maximal prime ideals in the integral closure of R in its field of quotients.
Dans cette note, nous allons montrer que, si est un anneau local intègre tel que ses fibres formelles soient géométriquement normales, alors le nombre des idéaux premiers minimaux dans la complétion -adique égale exactement le nombre dʼidéaux maximaux dans la clôture algébrique de R dans son corps de fractions.
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@article{CRMATH_2013__351_5-6_173_0, author = {Beddani, Charef}, title = {Note on the completion of a local domain with geometrically normal formal fibers}, journal = {Comptes Rendus. Math\'ematique}, pages = {173--175}, publisher = {Elsevier}, volume = {351}, number = {5-6}, year = {2013}, doi = {10.1016/j.crma.2013.03.004}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2013.03.004/} }
TY - JOUR AU - Beddani, Charef TI - Note on the completion of a local domain with geometrically normal formal fibers JO - Comptes Rendus. Mathématique PY - 2013 SP - 173 EP - 175 VL - 351 IS - 5-6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2013.03.004/ DO - 10.1016/j.crma.2013.03.004 LA - en ID - CRMATH_2013__351_5-6_173_0 ER -
%0 Journal Article %A Beddani, Charef %T Note on the completion of a local domain with geometrically normal formal fibers %J Comptes Rendus. Mathématique %D 2013 %P 173-175 %V 351 %N 5-6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2013.03.004/ %R 10.1016/j.crma.2013.03.004 %G en %F CRMATH_2013__351_5-6_173_0
Beddani, Charef. Note on the completion of a local domain with geometrically normal formal fibers. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 173-175. doi : 10.1016/j.crma.2013.03.004. http://archive.numdam.org/articles/10.1016/j.crma.2013.03.004/
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