{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:22:41Z","timestamp":1776784961139,"version":"3.51.2"},"reference-count":11,"publisher":"American Mathematical Society (AMS)","issue":"253","license":[{"start":{"date-parts":[[2006,9,1]],"date-time":"2006-09-01T00:00:00Z","timestamp":1157068800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n We give an algorithm for constructing normal integral bases of tame Galois extensions of the rationals with group\n \n \n \n \n A<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n A_4<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . Using earlier works we can do the same until degree\n \n \n \n 15<\/mml:mn>\n 15<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/s0025-5718-05-01779-5","type":"journal-article","created":{"date-parts":[[2005,11,16]],"date-time":"2005-11-16T10:22:35Z","timestamp":1132136555000},"page":"485-496","source":"Crossref","is-referenced-by-count":1,"title":["Normal integral bases for \ud835\udc34\u2084 extensions of the rationals"],"prefix":"10.1090","volume":"75","author":[{"given":"Jean","family":"Cougnard","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,9,1]]},"reference":[{"key":"1","first-page":"19","article-title":"Questions de base minimale dans la th\u00e9orie des nombres alg\u00e9briques","author":"Artin, E.","year":"1950"},{"key":"2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.24033\/asens.934","article-title":"Arithm\u00e9tique des corps ab\u00e9liens du troisi\u00e8me degr\u00e9","volume":"63","author":"Ch\u00e2telet, Albert","year":"1946","journal-title":"Ann. Sci. \\'{E}cole Norm. Sup. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0012-9593","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"163","DOI":"10.5802\/jtnb.224","article-title":"Anneaux d\u2019entiers stablement libres sur \u2124[\u210d\u2088\u00d7\u2102\u2082]","volume":"10","author":"Cougnard, Jean","year":"1998","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"399","DOI":"10.5802\/jtnb.286","article-title":"Construction de base normale pour les extensions de \ud835\udc44 \u00e0 groupe \ud835\udc37\u2084","volume":"12","author":"Cougnard, Jean","year":"2000","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"87","DOI":"10.5802\/jtnb.348","article-title":"Construction de bases normales pour les extensions galoisiennes absolues \u00e0 groupe de Galois quaternionien d\u2019ordre 12","volume":"14","author":"Cougnard, Jean","year":"2002","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"key":"6","series-title":"Pure and Applied Mathematics (New York)","isbn-type":"print","volume-title":"Methods of representation theory. Vol. II","author":"Curtis, Charles W.","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/0471888710"},{"key":"7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5802\/aif.307","article-title":"Sur l\u2019arithm\u00e9tique des extensions galoisiennes \u00e0 groupe de Galois di\u00e9dral d\u2019ordre 2\ud835\udc5d","volume":"19","author":"Martinet, Jacques","year":"1969","journal-title":"Ann. Inst. Fourier (Grenoble)","ISSN":"https:\/\/id.crossref.org\/issn\/0373-0956","issn-type":"print"},{"key":"8","unstructured":"C. BATUT, K. BELABAS, D. BERNARDI, H. COHEN, and M. OLIVIER. User\u2019s Guide to Pari-GP, version 2.02.12 (1999)."},{"key":"9","doi-asserted-by":"crossref","first-page":"445","DOI":"10.24033\/asens.1169","article-title":"Crit\u00e8re de d\u00e9composition d\u2019une extension de Kummer sur un sous-corps du corps de base","volume":"1","author":"Payan, Jean-Jacques","year":"1968","journal-title":"Ann. Sci. \\'{E}cole Norm. Sup. (4)","ISSN":"https:\/\/id.crossref.org\/issn\/0012-9593","issn-type":"print"},{"key":"10","doi-asserted-by":"publisher","first-page":"700","DOI":"10.2307\/1970033","article-title":"Modules over finite groups","volume":"69","author":"Rim, Dock Sang","year":"1959","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"11","first-page":"501","article-title":"Remarks on class groups of integral group rings","author":"Reiner, I.","year":"1974"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2006-75-253\/S0025-5718-05-01779-5\/S0025-5718-05-01779-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-253\/S0025-5718-05-01779-5\/S0025-5718-05-01779-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:34:23Z","timestamp":1776782063000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-253\/S0025-5718-05-01779-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9,1]]},"references-count":11,"journal-issue":{"issue":"253","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["S0025-5718-05-01779-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-05-01779-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2005,9,1]]}}}