{"type":"standard","title":"Projective line over a ring","displaytitle":"Projective line over a ring","namespace":{"id":0,"text":""},"wikibase_item":"Q7249472","titles":{"canonical":"Projective_line_over_a_ring","normalized":"Projective line over a ring","display":"Projective line over a ring"},"pageid":1271901,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Projectivisation_F7P%5E1.svg/330px-Projectivisation_F7P%5E1.svg.png","width":320,"height":320},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Projectivisation_F7P%5E1.svg/672px-Projectivisation_F7P%5E1.svg.png","width":672,"height":672},"lang":"en","dir":"ltr","revision":"1281572828","tid":"627baa5b-0610-11f0-88d4-ad72c48bcb05","timestamp":"2025-03-21T04:53:09Z","description":"Projective construction in ring theory","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Projective_line_over_a_ring","revisions":"https://en.wikipedia.org/wiki/Projective_line_over_a_ring?action=history","edit":"https://en.wikipedia.org/wiki/Projective_line_over_a_ring?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Projective_line_over_a_ring"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Projective_line_over_a_ring","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Projective_line_over_a_ring","edit":"https://en.m.wikipedia.org/wiki/Projective_line_over_a_ring?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Projective_line_over_a_ring"}},"extract":"In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A (with 1), the projective line P1(A) over A consists of points identified by projective coordinates. Let A× be the group of units of A; pairs (a, b) and (c, d) from A × A are related when there is a u in A× such that ua = c and ub = d. This relation is an equivalence relation. A typical equivalence class is written U[a, b].","extract_html":"
In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A (with 1), the projective line P1(A) over A consists of points identified by projective coordinates. Let A× be the group of units of A; pairs (a, b) and (c, d) from A × A are related when there is a u in A× such that ua = c and ub = d. This relation is an equivalence relation. A typical equivalence class is written U[a, b].
"}{"fact":"Researchers are unsure exactly how a cat purrs. Most veterinarians believe that a cat purrs by vibrating vocal folds deep in the throat. To do this, a muscle in the larynx opens and closes the air passage about 25 times per second.","length":231}
{"type":"standard","title":"Pan Wei-lun","displaytitle":"Pan Wei-lun","namespace":{"id":0,"text":""},"wikibase_item":"Q6136252","titles":{"canonical":"Pan_Wei-lun","normalized":"Pan Wei-lun","display":"Pan Wei-lun"},"pageid":8917919,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/2008LeisureTaiwan_Day2_ESPN_Wei-lun_Pan.jpg/330px-2008LeisureTaiwan_Day2_ESPN_Wei-lun_Pan.jpg","width":320,"height":240},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/1/1d/2008LeisureTaiwan_Day2_ESPN_Wei-lun_Pan.jpg","width":2304,"height":1728},"lang":"en","dir":"ltr","revision":"1297106516","tid":"1894d9a1-50bb-11f0-934a-aca7c1693ffe","timestamp":"2025-06-24T05:21:35Z","description":"Taiwanese baseball player (born 1982)","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Pan_Wei-lun","revisions":"https://en.wikipedia.org/wiki/Pan_Wei-lun?action=history","edit":"https://en.wikipedia.org/wiki/Pan_Wei-lun?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Pan_Wei-lun"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Pan_Wei-lun","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Pan_Wei-lun","edit":"https://en.m.wikipedia.org/wiki/Pan_Wei-lun?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Pan_Wei-lun"}},"extract":"Pan Wei-lun is a Taiwanese former professional baseball pitcher. He played in the Chinese Professional Baseball League (CPBL) for the Uni-President Lions from 2003 to 2024.","extract_html":"
Pan Wei-lun is a Taiwanese former professional baseball pitcher. He played in the Chinese Professional Baseball League (CPBL) for the Uni-President Lions from 2003 to 2024.
"}["Single-origin coffee unicorn cloud bread photo booth ennui, kitsch typewriter blackbird spyplane vaporware swag. Fashion axe ugh everyday carry celiac, banjo schlitz single-origin coffee polaroid wayfarers. La croix chicharrones tousled post-ironic af pabst XOXO tilde, meditation freegan. Mukbang sartorial drinking vinegar wolf ennui live-edge locavore vaporware quinoa man braid cloud bread. Authentic tumblr post-ironic squid neutral milk hotel. Gentrify four dollar toast big mood, marfa fixie DIY twee fashion axe cliche offal food truck everyday carry jean shorts selfies grailed.","Jawn copper mug ugh art party cred keytar 90's etsy XOXO raclette semiotics locavore. Cronut vegan subway tile ramps chartreuse. Umami gorpcore sustainable, butcher fixie trust fund organic hoodie kinfolk. Kombucha enamel pin shaman coloring book, offal synth lo-fi next level hashtag copper mug ethical kitsch polaroid street art. Sartorial selvage mumblecore, keytar shaman offal ethical. Occupy williamsburg blog poke hoodie.","Lo-fi typewriter YOLO plaid marfa tonx venmo cliche quinoa af copper mug fit twee. Locavore aesthetic etsy forage bespoke, hoodie hashtag lumbersexual. Dreamcatcher chartreuse sustainable mumblecore photo booth pitchfork. Helvetica vegan fingerstache forage. Adaptogen schlitz tonx, you probably haven't heard of them solarpunk pinterest Brooklyn enamel pin selvage unicorn PBR&B. Cliche disrupt lo-fi, sartorial neutra humblebrag meh pour-over hashtag microdosing iceland food truck forage. Dreamcatcher biodiesel pabst banjo tonx cronut you probably haven't heard of them fixie activated charcoal hammock seitan YOLO.","Pork belly banh mi tumeric franzen. Kombucha enamel pin messenger bag, tofu VHS normcore 8-bit man braid green juice humblebrag. Selfies chambray 90's single-origin coffee bespoke vaporware venmo. Offal letterpress taxidermy 3 wolf moon succulents, neutra tattooed fashion axe pop-up quinoa next level vape hella pabst health goth. Sriracha enamel pin XOXO humblebrag crucifix aesthetic marfa ugh franzen bruh sus vinyl portland.","Tofu squid hella, trust fund palo santo blackbird spyplane same plaid etsy beard literally cronut lumbersexual. Shaman kickstarter bushwick, mixtape edison bulb mustache chartreuse bruh blackbird spyplane authentic solarpunk. Fit mlkshk taxidermy PBR&B single-origin coffee tumeric ascot sriracha raclette copper mug. Taxidermy tattooed sartorial gatekeep meggings coloring book blue bottle lomo keffiyeh waistcoat chicharrones 90's la croix blog sustainable. Freegan synth godard, tbh polaroid meggings four loko cloud bread. Next level trust fund PBR&B echo park chartreuse. Pabst tumeric kickstarter post-ironic asymmetrical."]