{"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":"627bb242-0610-11f0-b505-f39fc3e96730","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":"The most popular pedigreed cat is the Persian cat, followed by the Main Coon cat and the Siamese cat.","length":101}
{"type":"standard","title":"Ersin Demir","displaytitle":"Ersin Demir","namespace":{"id":0,"text":""},"wikibase_item":"Q871056","titles":{"canonical":"Ersin_Demir","normalized":"Ersin Demir","display":"Ersin Demir"},"pageid":20447571,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Demir%2C_Ersin_FCI_08-09_WP.JPG/330px-Demir%2C_Ersin_FCI_08-09_WP.JPG","width":320,"height":480},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/a/a6/Demir%2C_Ersin_FCI_08-09_WP.JPG","width":1251,"height":1875},"lang":"en","dir":"ltr","revision":"1244754500","tid":"78c6d92d-6e41-11ef-a2ea-c833c001f228","timestamp":"2024-09-09T00:21:35Z","description":"Turkish footballer","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Ersin_Demir","revisions":"https://en.wikipedia.org/wiki/Ersin_Demir?action=history","edit":"https://en.wikipedia.org/wiki/Ersin_Demir?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Ersin_Demir"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Ersin_Demir","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Ersin_Demir","edit":"https://en.m.wikipedia.org/wiki/Ersin_Demir?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Ersin_Demir"}},"extract":"Ersin Demir is a Turkish football coach and former player, who most recently was the manager of FC Ingolstadt 04 II.","extract_html":"
Ersin Demir is a Turkish football coach and former player, who most recently was the manager of FC Ingolstadt 04 II.
"}{"fact":"Most cats adore sardines.","length":25}
{"slip": { "id": 35, "advice": "Only those who attempt the impossible can achieve the absurd."}}
{"slip": { "id": 33, "advice": "Don't let the bastards grind you down."}}
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