{"id":3287,"date":"2013-07-02T11:14:10","date_gmt":"2013-07-02T11:14:10","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3287"},"modified":"2013-07-02T11:14:10","modified_gmt":"2013-07-02T11:14:10","slug":"lemma-of-the-day-4","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3287","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let A be a ring. Let I &sub; J &sub; A be ideals. If M is J-adically complete and I is finitely generated, then M is I-adically complete. See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/090T\">Tag 090T<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let A be a ring. Let I &sub; J &sub; A be ideals. If M is J-adically complete and I is finitely generated, then M is I-adically complete. See Tag 090T.<\/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-3287","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\/3287","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=3287"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3287\/revisions"}],"predecessor-version":[{"id":3320,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3287\/revisions\/3320"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}