22:
512:
1143:
404:
291:
1884:
2056:
547:
769:
662:
1947:
1812:
1767:
1601:
1550:
1423:
1368:
1316:
1252:
999:
946:
853:
1480:
1689:
430:
1718:
1646:
1261:
to the conductor share many of pleasant properties of ideals in
Dedekind domains. Furthermore, for these ideals there is a tight correspondence between ideals of
1038:
2325:, so for orders of quadratic number fields, the index may be identified with the conductor. This identification fails for higher degree number fields.
1318:
have unique factorization into products of invertible prime ideals that are coprime to the conductor. In particular, all such ideals are invertible.
39:
1953:
All of these properties fail in general for ideals not coprime to the conductor. To see some of the difficulties that may arise, assume that
332:
219:
2351:
105:
86:
58:
65:
43:
1213:
does not have unique factorization into prime ideals, and the failure of unique factorization is measured by the conductor
569:. Therefore the non-zero elements of the conductor are those that suffice as common denominators when writing elements of
2390:
2005:
72:
2276:
1817:
54:
32:
1153:
323:
520:
727:
617:
1776:
1731:
1565:
1514:
1387:
1332:
1280:
1216:
963:
910:
817:
165:
1431:
1025:
2083:, then the same reasoning applies. But the left-hand side of the above equation makes no reference to
1662:
2385:
507:{\displaystyle \{0\}\cup \left\{a\in A\setminus \{0\}:B\subseteq \textstyle {\frac {1}{a}}A\right\},}
315:
143:
1889:
168:. One interpretation of the conductor is that it measures the failure of unique factorization into
2126:
211:
157:
79:
1694:
1606:
150:
139:
2347:
1814:. This bijection preserves the property of being prime. It is also multiplicative, that is,
1426:
2370:
1970:
1258:
949:
161:
146:
131:
153:, and then the conductor measures the failure of the smaller ring to be integrally closed.
1172:
421:
307:
676:
2379:
2235:
1138:{\displaystyle S^{-1}{\mathfrak {f}}(B/A)\subseteq {\mathfrak {f}}(S^{-1}B/S^{-1}A),}
1202:
1190:
697:
1965:(in particular, it is contained in, hence not coprime to, the conductor). Then
1483:
169:
123:
119:
21:
771:. In this case, the conductor is non-zero. This applies in particular when
1721:
2221:, so it is contained in the conductor. On the other hand, the ideals of
2184:
135:
1201:
can be the affine coordinate ring of a smooth projective curve over a
409:
Because the conductor is defined as an annihilator, it is an ideal of
1167:
Some of the most important applications of the conductor arise when
399:{\displaystyle {\mathfrak {f}}(B/A)=\{a\in A\colon aB\subseteq A\}.}
286:{\displaystyle {\mathfrak {f}}(B/A)=\operatorname {Ann} _{A}(B/A).}
156:
The conductor is of great importance in the study of non-maximal
15:
1209:
the affine coordinate ring of a singular model. The ring
775:
is the ring of integers in an algebraic number field and
557:
is non-zero and in the conductor, then every element of
524:
481:
2296:. Under this isomorphism, the conductor annihilates
2091:, only to their shared fraction field, and therefore
2008:
1892:
1820:
1779:
1734:
1697:
1665:
1609:
1568:
1517:
1434:
1390:
1335:
1283:
1219:
1041:
966:
913:
820:
730:
620:
523:
433:
335:
222:
1013:contained in the conductor which are not ideals of
885:is contained in the conductor. Indeed, for such a
561:may be written as a fraction whose numerator is in
549:is considered as a subset of the fraction field of
46:. Unsourced material may be challenged and removed.
2050:
1941:
1878:
1806:
1761:
1712:
1683:
1640:
1595:
1544:
1474:
1417:
1362:
1310:
1246:
1137:
993:
940:
847:
763:
656:
541:
506:
398:
285:
2061:since we may multiply both sides of the equation
2051:{\displaystyle \{x\in K\colon xJ\subseteq J\}=B,}
2190:. The conductor of this order equals the ideal
956:, so any ideal contained in it is contained in
1879:{\displaystyle (I\cap A)(I'\cap A)=II'\cap A}
326:. More concretely, the conductor is the set
8:
2036:
2009:
648:
621:
469:
463:
440:
434:
390:
363:
1009:. (It can happen that there are ideals of
2321:In this case, the index is also equal to
542:{\displaystyle \textstyle {\frac {1}{a}}A}
2007:
1891:
1819:
1793:
1781:
1780:
1778:
1748:
1736:
1735:
1733:
1696:
1664:
1627:
1613:
1608:
1582:
1570:
1569:
1567:
1531:
1519:
1518:
1516:
1464:
1438:
1433:
1404:
1392:
1391:
1389:
1349:
1337:
1336:
1334:
1297:
1285:
1284:
1282:
1233:
1221:
1220:
1218:
1117:
1108:
1096:
1083:
1082:
1068:
1056:
1055:
1046:
1040:
980:
968:
967:
965:
927:
915:
914:
912:
834:
822:
821:
819:
764:{\displaystyle m\in {\mathfrak {f}}(B/A)}
750:
738:
737:
729:
657:{\displaystyle \{r\in R:rB\subseteq A\}.}
619:
525:
522:
482:
432:
424:, then the conductor may be rewritten as
349:
337:
336:
334:
269:
254:
236:
224:
223:
221:
106:Learn how and when to remove this message
2334:
2144:be its ring of integers. By extending
604:its field of fractions. Then, because
460:
2117:Conductors of quadratic number fields
7:
2262:. The latter ring is isomorphic to
2101:. Therefore being an ideal of both
1807:{\displaystyle {\mathfrak {f}}(B/A)}
1762:{\displaystyle {\mathfrak {f}}(B/A)}
1596:{\displaystyle {\mathfrak {f}}(B/A)}
1545:{\displaystyle {\mathfrak {f}}(B/A)}
1418:{\displaystyle {\mathfrak {f}}(B/A)}
1363:{\displaystyle {\mathfrak {f}}(B/A)}
1311:{\displaystyle {\mathfrak {f}}(B/A)}
1247:{\displaystyle {\mathfrak {f}}(B/A)}
994:{\displaystyle {\mathfrak {f}}(B/A)}
941:{\displaystyle {\mathfrak {f}}(B/A)}
848:{\displaystyle {\mathfrak {f}}(B/A)}
130:is a measurement of how far apart a
44:adding citations to reliable sources
1782:
1737:
1648:is an isomorphism. In particular,
1571:
1520:
1393:
1338:
1286:
1222:
1084:
1057:
969:
916:
823:
739:
338:
225:
1603:and the natural ring homomorphism
1475:{\displaystyle A/(I\cap A)\to B/I}
792:The conductor is also an ideal of
14:
1189:can be the ring of integers of a
779:is an order (a subring for which
696:. Otherwise, the conductor is a
611:, the conductor is also equal to
188:be commutative rings, and assume
2160:-basis, we see that every order
1684:{\displaystyle I\mapsto I\cap A}
672:The conductor is the whole ring
20:
1148:with equality in the case that
952:, the conductor is an ideal of
686:and, therefore, if and only if
31:needs additional citations for
2234:are the same as ideals of the
1942:{\displaystyle (JB)(J'B)=JJ'B}
1919:
1905:
1902:
1893:
1853:
1836:
1833:
1821:
1801:
1787:
1756:
1742:
1701:
1669:
1621:
1590:
1576:
1539:
1525:
1458:
1455:
1443:
1412:
1398:
1357:
1343:
1305:
1291:
1241:
1227:
1163:Conductors of Dedekind domains
1129:
1089:
1076:
1062:
988:
974:
935:
921:
842:
828:
758:
744:
357:
343:
277:
263:
244:
230:
1:
2109:implies non-invertibility in
1277:that are relatively prime to
138:are. Most often, the larger
2199:. Indeed, it is clear that
1957:is a non-zero ideal of both
1562:that is relatively prime to
1511:that is relatively prime to
1384:that is relatively prime to
1329:that is relatively prime to
573:as quotients of elements of
55:"Conductor" ring theory
1713:{\displaystyle J\mapsto JB}
1641:{\displaystyle A/J\to B/JB}
2407:
2342:Bourbaki, Nicolas (1989).
2277:second isomorphism theorem
1197:a non-maximal order. Or,
1005:which is also an ideal of
960:. This fact implies that
2346:. Springer. p. 316.
1185:is finite. For example,
565:and whose denominator is
2279:, so all such ideals of
1969:cannot be an invertible
1652:is prime if and only if
1490:is prime if and only if
1001:is the largest ideal of
2252:) /
2079:is also invertible in
2052:
1991:is a Dedekind domain,
1943:
1880:
1808:
1763:
1714:
1685:
1642:
1597:
1546:
1476:
1419:
1364:
1312:
1248:
1139:
995:
942:
849:
765:
658:
600:might be a domain and
543:
508:
400:
287:
166:algebraic number field
2053:
1944:
1881:
1809:
1764:
1715:
1686:
1643:
1598:
1547:
1477:
1420:
1365:
1313:
1249:
1140:
1026:multiplicative subset
996:
943:
869:. In fact, an ideal
850:
766:
668:Elementary properties
659:
584:is a ring containing
544:
509:
401:
288:
2006:
1890:
1818:
1777:
1773:relatively prime to
1732:
1728:relatively prime to
1695:
1663:
1607:
1566:
1515:
1432:
1388:
1333:
1281:
1217:
1039:
964:
911:
818:
728:
618:
521:
431:
333:
220:
40:improve this article
2391:Commutative algebra
2344:Commutative Algebra
2127:quadratic extension
903:, so by definition
796:, because, for any
2183:for some positive
2048:
1939:
1876:
1804:
1759:
1724:between ideals of
1710:
1681:
1638:
1593:
1542:
1486:. In particular,
1472:
1415:
1360:
1308:
1244:
1154:finitely generated
1135:
991:
938:
845:
761:
654:
539:
538:
504:
495:
396:
283:
151:field of fractions
2292:with an ideal of
1995:is invertible in
1427:ring homomorphism
533:
490:
147:integrally closed
116:
115:
108:
90:
2398:
2371:Integral element
2358:
2357:
2339:
2317:
2309:, so it must be
2308:
2274:
2261:
2182:
2155:
2143:
2100:
2070:
2057:
2055:
2054:
2049:
1999:, and therefore
1986:
1971:fractional ideal
1948:
1946:
1945:
1940:
1935:
1915:
1885:
1883:
1882:
1877:
1869:
1846:
1813:
1811:
1810:
1805:
1797:
1786:
1785:
1768:
1766:
1765:
1760:
1752:
1741:
1740:
1719:
1717:
1716:
1711:
1690:
1688:
1687:
1682:
1647:
1645:
1644:
1639:
1631:
1617:
1602:
1600:
1599:
1594:
1586:
1575:
1574:
1557:
1551:
1549:
1548:
1543:
1535:
1524:
1523:
1499:
1481:
1479:
1478:
1473:
1468:
1442:
1425:and the natural
1424:
1422:
1421:
1416:
1408:
1397:
1396:
1379:
1369:
1367:
1366:
1361:
1353:
1342:
1341:
1317:
1315:
1314:
1309:
1301:
1290:
1289:
1253:
1251:
1250:
1245:
1237:
1226:
1225:
1184:
1144:
1142:
1141:
1136:
1125:
1124:
1112:
1104:
1103:
1088:
1087:
1072:
1061:
1060:
1054:
1053:
1000:
998:
997:
992:
984:
973:
972:
947:
945:
944:
939:
931:
920:
919:
907:is contained in
902:
877:is contained in
868:
854:
852:
851:
846:
838:
827:
826:
813:
807:
801:
788:
770:
768:
767:
762:
754:
743:
742:
723:
714:is finite, then
713:
695:
685:
663:
661:
660:
655:
610:
588:. For example,
548:
546:
545:
540:
534:
526:
513:
511:
510:
505:
500:
496:
491:
483:
405:
403:
402:
397:
353:
342:
341:
321:
305:
292:
290:
289:
284:
273:
259:
258:
240:
229:
228:
197:
162:ring of integers
132:commutative ring
111:
104:
100:
97:
91:
89:
48:
24:
16:
2406:
2405:
2401:
2400:
2399:
2397:
2396:
2395:
2376:
2375:
2367:
2362:
2361:
2354:
2341:
2340:
2336:
2331:
2310:
2301: /
2297:
2291:
2283:are the sum of
2267: /
2263:
2260:
2251:
2238:
2233:
2216:
2208:is an ideal of
2207:
2198:
2181:
2169:
2154:
2145:
2142:
2134:
2119:
2092:
2062:
2004:
2003:
1978:
1928:
1908:
1888:
1887:
1862:
1839:
1816:
1815:
1775:
1774:
1730:
1729:
1693:
1692:
1661:
1660:
1605:
1604:
1564:
1563:
1558:is an ideal of
1553:
1513:
1512:
1507:is an ideal of
1491:
1430:
1429:
1386:
1385:
1380:is an ideal of
1371:
1331:
1330:
1325:is an ideal of
1279:
1278:
1215:
1214:
1176:
1173:Dedekind domain
1165:
1113:
1092:
1042:
1037:
1036:
962:
961:
909:
908:
890:
881:if and only if
856:
816:
815:
809:
803:
797:
780:
726:
725:
715:
708:
687:
680:
670:
616:
615:
605:
553:. That is, if
519:
518:
450:
446:
429:
428:
422:integral domain
331:
330:
319:
306:is viewed as a
297:
250:
218:
217:
189:
178:
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
2404:
2402:
2394:
2393:
2388:
2378:
2377:
2374:
2373:
2366:
2363:
2360:
2359:
2352:
2333:
2332:
2330:
2327:
2287:
2256:
2247:
2229:
2212:
2203:
2194:
2177:
2150:
2138:
2118:
2115:
2059:
2058:
2047:
2044:
2041:
2038:
2035:
2032:
2029:
2026:
2023:
2020:
2017:
2014:
2011:
1951:
1950:
1938:
1934:
1931:
1927:
1924:
1921:
1918:
1914:
1911:
1907:
1904:
1901:
1898:
1895:
1875:
1872:
1868:
1865:
1861:
1858:
1855:
1852:
1849:
1845:
1842:
1838:
1835:
1832:
1829:
1826:
1823:
1803:
1800:
1796:
1792:
1789:
1784:
1769:and ideals of
1758:
1755:
1751:
1747:
1744:
1739:
1709:
1706:
1703:
1700:
1680:
1677:
1674:
1671:
1668:
1659:The functions
1657:
1637:
1634:
1630:
1626:
1623:
1620:
1616:
1612:
1592:
1589:
1585:
1581:
1578:
1573:
1541:
1538:
1534:
1530:
1527:
1522:
1501:
1471:
1467:
1463:
1460:
1457:
1454:
1451:
1448:
1445:
1441:
1437:
1414:
1411:
1407:
1403:
1400:
1395:
1359:
1356:
1352:
1348:
1345:
1340:
1319:
1307:
1304:
1300:
1296:
1293:
1288:
1273:The ideals of
1265:and ideals of
1243:
1240:
1236:
1232:
1229:
1224:
1164:
1161:
1146:
1145:
1134:
1131:
1128:
1123:
1120:
1116:
1111:
1107:
1102:
1099:
1095:
1091:
1086:
1081:
1078:
1075:
1071:
1067:
1064:
1059:
1052:
1049:
1045:
990:
987:
983:
979:
976:
971:
937:
934:
930:
926:
923:
918:
844:
841:
837:
833:
830:
825:
760:
757:
753:
749:
746:
741:
736:
733:
677:if and only if
669:
666:
665:
664:
653:
650:
647:
644:
641:
638:
635:
632:
629:
626:
623:
537:
532:
529:
515:
514:
503:
499:
494:
489:
486:
480:
477:
474:
471:
468:
465:
462:
459:
456:
453:
449:
445:
442:
439:
436:
407:
406:
395:
392:
389:
386:
383:
380:
377:
374:
371:
368:
365:
362:
359:
356:
352:
348:
345:
340:
294:
293:
282:
279:
276:
272:
268:
265:
262:
257:
253:
249:
246:
243:
239:
235:
232:
227:
177:
174:
136:extension ring
122:, a branch of
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
2403:
2392:
2389:
2387:
2384:
2383:
2381:
2372:
2369:
2368:
2364:
2355:
2353:0-387-19371-5
2349:
2345:
2338:
2335:
2328:
2326:
2324:
2319:
2316:
2313:
2307:
2304:
2300:
2295:
2290:
2286:
2282:
2278:
2273:
2270:
2266:
2259:
2255:
2250:
2246:
2242:
2237:
2236:quotient ring
2232:
2228:
2224:
2220:
2217:contained in
2215:
2211:
2206:
2202:
2197:
2193:
2189:
2186:
2180:
2176:
2172:
2168:has the form
2167:
2163:
2159:
2153:
2149:
2141:
2137:
2132:
2128:
2124:
2116:
2114:
2112:
2108:
2104:
2099:
2095:
2090:
2086:
2082:
2078:
2074:
2069:
2065:
2045:
2042:
2039:
2033:
2030:
2027:
2024:
2021:
2018:
2015:
2012:
2002:
2001:
2000:
1998:
1994:
1990:
1985:
1981:
1976:
1972:
1968:
1964:
1960:
1956:
1936:
1932:
1929:
1925:
1922:
1916:
1912:
1909:
1899:
1896:
1873:
1870:
1866:
1863:
1859:
1856:
1850:
1847:
1843:
1840:
1830:
1827:
1824:
1798:
1794:
1790:
1772:
1753:
1749:
1745:
1727:
1723:
1707:
1704:
1698:
1678:
1675:
1672:
1666:
1658:
1655:
1651:
1635:
1632:
1628:
1624:
1618:
1614:
1610:
1587:
1583:
1579:
1561:
1556:
1536:
1532:
1528:
1510:
1506:
1502:
1498:
1494:
1489:
1485:
1469:
1465:
1461:
1452:
1449:
1446:
1439:
1435:
1428:
1409:
1405:
1401:
1383:
1378:
1374:
1354:
1350:
1346:
1328:
1324:
1320:
1302:
1298:
1294:
1276:
1272:
1271:
1270:
1268:
1264:
1260:
1255:
1238:
1234:
1230:
1212:
1208:
1204:
1200:
1196:
1192:
1188:
1183:
1179:
1174:
1170:
1162:
1160:
1158:
1155:
1151:
1132:
1126:
1121:
1118:
1114:
1109:
1105:
1100:
1097:
1093:
1079:
1073:
1069:
1065:
1050:
1047:
1043:
1035:
1034:
1033:
1031:
1027:
1023:
1020:Suppose that
1018:
1016:
1012:
1008:
1004:
985:
981:
977:
959:
955:
951:
932:
928:
924:
906:
901:
897:
893:
888:
884:
880:
876:
872:
867:
863:
859:
839:
835:
831:
812:
806:
800:
795:
790:
787:
783:
778:
774:
755:
751:
747:
734:
731:
722:
718:
711:
707:If the index
705:
703:
699:
694:
690:
684:
678:
675:
667:
651:
645:
642:
639:
636:
633:
630:
627:
624:
614:
613:
612:
609:
603:
599:
595:
591:
587:
583:
578:
576:
572:
568:
564:
560:
556:
552:
535:
530:
527:
501:
497:
492:
487:
484:
478:
475:
472:
466:
457:
454:
451:
447:
443:
437:
427:
426:
425:
423:
419:
414:
412:
393:
387:
384:
381:
378:
375:
372:
369:
366:
360:
354:
350:
346:
329:
328:
327:
325:
317:
313:
309:
304:
300:
280:
274:
270:
266:
260:
255:
251:
247:
241:
237:
233:
216:
215:
214:
213:
209:
205:
201:
196:
192:
187:
183:
175:
173:
171:
167:
163:
159:
154:
152:
148:
145:
141:
137:
133:
129:
125:
121:
110:
107:
99:
96:February 2018
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
2343:
2337:
2322:
2320:
2314:
2311:
2305:
2302:
2298:
2293:
2288:
2284:
2280:
2271:
2268:
2264:
2257:
2253:
2248:
2244:
2240:
2230:
2226:
2222:
2218:
2213:
2209:
2204:
2200:
2195:
2191:
2187:
2178:
2174:
2170:
2165:
2161:
2157:
2151:
2147:
2139:
2135:
2130:
2122:
2120:
2110:
2106:
2102:
2097:
2093:
2088:
2084:
2080:
2076:
2072:
2067:
2063:
2060:
1996:
1992:
1988:
1983:
1979:
1974:
1966:
1962:
1958:
1954:
1952:
1770:
1725:
1653:
1649:
1559:
1554:
1508:
1504:
1496:
1492:
1487:
1381:
1376:
1372:
1326:
1322:
1274:
1266:
1262:
1256:
1210:
1206:
1203:finite field
1198:
1194:
1191:number field
1186:
1181:
1177:
1168:
1166:
1156:
1149:
1147:
1029:
1021:
1019:
1014:
1010:
1006:
1002:
957:
953:
904:
899:
895:
891:
886:
882:
878:
874:
870:
865:
861:
857:
810:
804:
798:
793:
791:
789:is finite).
785:
781:
776:
772:
720:
716:
709:
706:
701:
698:proper ideal
692:
688:
682:
679:it contains
673:
671:
607:
601:
597:
593:
592:might equal
589:
585:
581:
579:
574:
570:
566:
562:
558:
554:
550:
516:
417:
415:
410:
408:
322:denotes the
311:
302:
298:
295:
207:
203:
199:
194:
190:
185:
181:
179:
170:prime ideals
155:
127:
117:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
2386:Ring theory
2225:containing
1987:. Because
1484:isomorphism
324:annihilator
124:mathematics
120:ring theory
2380:Categories
2329:References
2133:, and let
950:Conversely
176:Definition
66:newspapers
2031:⊆
2022::
2016:∈
1871:∩
1848:∩
1828:∩
1722:bijection
1720:define a
1702:↦
1676:∩
1670:↦
1656:is prime.
1622:→
1500:is prime.
1459:→
1450:∩
1159:-module.
1119:−
1098:−
1080:⊆
1048:−
735:∈
643:⊆
628:∈
479:⊆
461:∖
455:∈
444:∪
385:⊆
376::
370:∈
261:
200:conductor
128:conductor
2365:See also
1933:′
1913:′
1867:′
1844:′
1180: /
1032:. Then
808:and any
784: /
580:Suppose
308:quotient
301: /
2275:by the
2185:integer
1977:unless
1552:, then
1370:, then
1259:coprime
1257:Ideals
316:modules
210:is the
198:. The
160:in the
149:in its
134:and an
80:scholar
2350:
2075:. If
1482:is an
517:where
420:is an
318:, and
164:of an
158:orders
144:domain
126:, the
82:
75:
68:
61:
53:
2156:to a
2125:be a
1171:is a
1152:is a
1024:is a
724:, so
596:, or
296:Here
212:ideal
142:is a
87:JSTOR
73:books
2348:ISBN
2146:1 ∈
2121:Let
2105:and
1961:and
1886:and
1691:and
1205:and
1193:and
1175:and
681:1 ∈
606:1 ∈
184:and
180:Let
140:ring
59:news
2164:in
2129:of
2087:or
2071:by
1973:of
1503:If
1321:If
1028:of
1017:.)
948:.
873:of
858:baB
814:in
802:in
700:of
416:If
320:Ann
310:of
252:Ann
206:in
202:of
118:In
42:by
2382::
2318:.
2285:cO
2254:cO
2245:cO
2243:+
2227:cO
2201:cO
2192:cO
2175:cO
2173:+
2113:.
2096:=
2066:⊆
2064:xJ
1982:=
1654:JB
1555:JB
1495:∩
1375:∩
1269::
1254:.
898:⊆
894:⊆
892:JB
889:,
864:⊆
862:aB
860:⊆
855:,
719:⊆
717:mB
712:=
704:.
691:=
577:.
413:.
193:⊆
172:.
2356:.
2323:c
2315:Z
2312:c
2306:Z
2303:c
2299:Z
2294:Z
2289:K
2281:O
2272:Z
2269:c
2265:Z
2258:K
2249:K
2241:Z
2239:(
2231:K
2223:O
2219:O
2214:K
2210:O
2205:K
2196:K
2188:c
2179:K
2171:Z
2166:K
2162:O
2158:Z
2152:K
2148:O
2140:K
2136:O
2131:Q
2123:K
2111:A
2107:B
2103:A
2098:B
2094:A
2089:B
2085:A
2081:A
2077:J
2073:J
2068:J
2046:,
2043:B
2040:=
2037:}
2034:J
2028:J
2025:x
2019:K
2013:x
2010:{
1997:B
1993:J
1989:B
1984:B
1980:A
1975:A
1967:J
1963:B
1959:A
1955:J
1949:.
1937:B
1930:J
1926:J
1923:=
1920:)
1917:B
1910:J
1906:(
1903:)
1900:B
1897:J
1894:(
1874:A
1864:I
1860:I
1857:=
1854:)
1851:A
1841:I
1837:(
1834:)
1831:A
1825:I
1822:(
1802:)
1799:A
1795:/
1791:B
1788:(
1783:f
1771:B
1757:)
1754:A
1750:/
1746:B
1743:(
1738:f
1726:A
1708:B
1705:J
1699:J
1679:A
1673:I
1667:I
1650:J
1636:B
1633:J
1629:/
1625:B
1619:J
1615:/
1611:A
1591:)
1588:A
1584:/
1580:B
1577:(
1572:f
1560:B
1540:)
1537:A
1533:/
1529:B
1526:(
1521:f
1509:A
1505:J
1497:A
1493:I
1488:I
1470:I
1466:/
1462:B
1456:)
1453:A
1447:I
1444:(
1440:/
1436:A
1413:)
1410:A
1406:/
1402:B
1399:(
1394:f
1382:A
1377:A
1373:I
1358:)
1355:A
1351:/
1347:B
1344:(
1339:f
1327:B
1323:I
1306:)
1303:A
1299:/
1295:B
1292:(
1287:f
1275:A
1267:A
1263:B
1242:)
1239:A
1235:/
1231:B
1228:(
1223:f
1211:A
1207:A
1199:B
1195:A
1187:B
1182:A
1178:B
1169:B
1157:A
1150:B
1133:,
1130:)
1127:A
1122:1
1115:S
1110:/
1106:B
1101:1
1094:S
1090:(
1085:f
1077:)
1074:A
1070:/
1066:B
1063:(
1058:f
1051:1
1044:S
1030:A
1022:S
1015:B
1011:A
1007:B
1003:A
989:)
986:A
982:/
978:B
975:(
970:f
958:A
954:A
936:)
933:A
929:/
925:B
922:(
917:f
905:J
900:A
896:J
887:J
883:J
879:A
875:B
871:J
866:A
843:)
840:A
836:/
832:B
829:(
824:f
811:a
805:B
799:b
794:B
786:A
782:B
777:A
773:B
759:)
756:A
752:/
748:B
745:(
740:f
732:m
721:A
710:m
702:A
693:B
689:A
683:A
674:A
652:.
649:}
646:A
640:B
637:r
634::
631:R
625:r
622:{
608:B
602:R
598:B
594:B
590:R
586:B
582:R
575:A
571:B
567:a
563:A
559:B
555:a
551:B
536:A
531:a
528:1
502:,
498:}
493:A
488:a
485:1
476:B
473::
470:}
467:0
464:{
458:A
452:a
448:{
441:}
438:0
435:{
418:B
411:A
394:.
391:}
388:A
382:B
379:a
373:A
367:a
364:{
361:=
358:)
355:A
351:/
347:B
344:(
339:f
314:-
312:A
303:A
299:B
281:.
278:)
275:A
271:/
267:B
264:(
256:A
248:=
245:)
242:A
238:/
234:B
231:(
226:f
208:B
204:A
195:B
191:A
186:B
182:A
109:)
103:(
98:)
94:(
84:·
77:·
70:·
63:·
36:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
