Let D be an integral domain and be the set of stable star operations of finite type on D. In this note, we show that if Ω is the set of nonzero prime ideals P of D with , then . We also show that if , then if and only if Ω is linearly ordered under inclusion; and if and only if each pair of elements in Ω are incomparable.
Soit D un anneau intègre et lʼensemble des opérations étoile, stables, de type fini sur D. Nous montrons dans cette note que, si Ω désigne lʼensemble des idéaux premiers non nuls P de D tels que , alors . Nous montrons également que, si , alors si et seulement si Ω est totalement ordonné par lʼinclusion et si et seulement si les éléments de Ω sont deux à deux incomparables.
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@article{CRMATH_2012__350_11-12_557_0, author = {Chang, Gyu Whan}, title = {On the cardinality of stable star operations of finite type on an integral domain}, journal = {Comptes Rendus. Math\'ematique}, pages = {557--560}, publisher = {Elsevier}, volume = {350}, number = {11-12}, year = {2012}, doi = {10.1016/j.crma.2012.05.015}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.05.015/} }
TY - JOUR AU - Chang, Gyu Whan TI - On the cardinality of stable star operations of finite type on an integral domain JO - Comptes Rendus. Mathématique PY - 2012 SP - 557 EP - 560 VL - 350 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.05.015/ DO - 10.1016/j.crma.2012.05.015 LA - en ID - CRMATH_2012__350_11-12_557_0 ER -
%0 Journal Article %A Chang, Gyu Whan %T On the cardinality of stable star operations of finite type on an integral domain %J Comptes Rendus. Mathématique %D 2012 %P 557-560 %V 350 %N 11-12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.05.015/ %R 10.1016/j.crma.2012.05.015 %G en %F CRMATH_2012__350_11-12_557_0
Chang, Gyu Whan. On the cardinality of stable star operations of finite type on an integral domain. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 557-560. doi : 10.1016/j.crma.2012.05.015. http://archive.numdam.org/articles/10.1016/j.crma.2012.05.015/
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