{"id":3355,"date":"2013-07-13T08:46:03","date_gmt":"2013-07-13T08:46:03","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3355"},"modified":"2013-07-13T08:46:03","modified_gmt":"2013-07-13T08:46:03","slug":"lemma-of-the-day-11","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3355","title":{"rendered":"Lemma of the day"},"content":{"rendered":"

Let R be a ring. Let x ∈ R. Assume<\/p>\n

    \n
  1. R is a normal Noetherian domain,<\/li>\n
  2. R\/xR is a Japanese domain,<\/li>\n
  3. R = lim R\/xn<\/sup>R is complete with respect to x.<\/li>\n<\/ol>\n

    Then R is Japanese. See Tag 032P<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Let R be a ring. Let x ∈ R. Assume R is a normal Noetherian domain, R\/xR is a Japanese domain, R = lim R\/xnR is complete with respect to x. Then R is Japanese. See Tag 032P.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3355","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3355","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3355"}],"version-history":[{"count":2,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3355\/revisions"}],"predecessor-version":[{"id":3357,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3355\/revisions\/3357"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3355"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3355"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}