{"id":3273,"date":"2013-06-28T21:03:21","date_gmt":"2013-06-28T21:03:21","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3273"},"modified":"2013-06-28T21:03:21","modified_gmt":"2013-06-28T21:03:21","slug":"lemma-of-the-day","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3273","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let A be a Noetherian ring and I &sub; A an ideal. For every n let M_n be a flat A\/I^n-module. Let M_{n + 1} &#8212;> M_n be a surjective A-module map. Then the inverse limit M =lim M_n is a flat A-module (see <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/0912\">Tag 0912<\/a>).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let A be a Noetherian ring and I &sub; A an ideal. For every n let M_n be a flat A\/I^n-module. Let M_{n + 1} &#8212;> M_n be a surjective A-module map. Then the inverse limit M =lim M_n is &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3273\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/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-3273","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\/3273","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=3273"}],"version-history":[{"count":4,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3273\/revisions"}],"predecessor-version":[{"id":3277,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3273\/revisions\/3277"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3273"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3273"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}