{"id":3339,"date":"2013-07-08T20:15:50","date_gmt":"2013-07-08T20:15:50","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3339"},"modified":"2013-07-08T20:15:50","modified_gmt":"2013-07-08T20:15:50","slug":"lemma-of-the-day-7","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3339","title":{"rendered":"Lemma of the day"},"content":{"rendered":"

Let R —> S be a ring map. Let p ⊂ R be a prime. Assume that<\/p>\n

    \n
  1. there exists a unique prime q ⊂ S lying over p, and<\/li>\n
  2. either\n
      \n
    1. going up holds for R —> S, or<\/li>\n
    2. going down holds for R —> S and there is at most one prime of S above every prime of R.<\/li>\n<\/ol>\n<\/ol>\n

      Then Sp<\/sub>=Sq<\/sub>. See Tag 00EA<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Let R —> S be a ring map. Let p ⊂ R be a prime. Assume that there exists a unique prime q ⊂ S lying over p, and either going up holds for R —> S, or going down … Continue reading →<\/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-3339","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\/3339","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=3339"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3339\/revisions"}],"predecessor-version":[{"id":3344,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3339\/revisions\/3344"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}