. . . "B\u00E9zout domain"@en . . "3131407"^^ . "\uAC00\uD658\uB300\uC218\uD559\uC5D0\uC11C \uBCA0\uC8FC \uC815\uC5ED(B\u00E9zout\u6574\u57DF, \uC601\uC5B4: B\u00E9zout domain)\uC740 \uBCA0\uC8FC \uD56D\uB4F1\uC2DD\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uC815\uC5ED\uC774\uB2E4."@ko . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u30D9\u30BA\u30FC\u6574\u57DF (B\u00E9zout domain) \u306F2\u3064\u306E\u4E3B\u30A4\u30C7\u30A2\u30EB\u306E\u548C\u304C\u518D\u3073\u4E3B\u30A4\u30C7\u30A2\u30EB\u306B\u306A\u308B\u3088\u3046\u306A\u6574\u57DF\u3067\u3042\u308B\u3002\u3053\u306E\u3053\u3068\u304C\u610F\u5473\u3059\u308B\u306E\u306F\u3001\u5143\u306E\u5404\u7D44\u306B\u5BFE\u3057\u3066\u30D9\u30BA\u30FC\u306E\u7B49\u5F0F (B\u00E9zout identity) \u304C\u6210\u308A\u7ACB\u3061\u3001\u3059\u3079\u3066\u306E\u6709\u9650\u751F\u6210\u30A4\u30C7\u30A2\u30EB\u306F\u5358\u9805\u3067\u3042\u308B\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308B\u3002\u4EFB\u610F\u306E\u5358\u9805\u30A4\u30C7\u30A2\u30EB\u6574\u57DF (PID) \u306F\u30D9\u30BA\u30FC\u6574\u57DF\u3060\u304C\u3001\u30D9\u30BA\u30FC\u6574\u57DF\u306F\u30CD\u30FC\u30BF\u30FC\u74B0\u3068\u306F\u9650\u3089\u306A\u3044\u306E\u3067\u3001\u6709\u9650\u751F\u6210\u3067\u306A\u3044\u30A4\u30C7\u30A2\u30EB\u3092\u3082\u3064\u304B\u3082\u3057\u308C\u306A\u3044\uFF08\u3053\u308C\u306F\u660E\u3089\u304B\u306B PID \u3067\u306A\u3044\uFF09\u3002\u305D\u3046\u3067\u3042\u308C\u3070\u3001\u4E00\u610F\u5206\u89E3\u6574\u57DF (UFD) \u3067\u306F\u306A\u3044\u304C\u3001\u306A\u304AGCD\u6574\u57DF\u3067\u3042\u308B\u3002\u30D9\u30BA\u30FC\u6574\u57DF\u306E\u7406\u8AD6\u306F PID \u306E\u6027\u8CEA\u306E\u591A\u304F\u3092\u3001\u30CD\u30FC\u30BF\u30FC\u6027\u3092\u8981\u6C42\u305B\u305A\u306B\u3001\u4FDD\u3064\u3002\u30D9\u30BA\u30FC\u6574\u57DF\u306F\u30D5\u30E9\u30F3\u30B9\u4EBA\u6570\u5B66\u8005 \u00C9tienne B\u00E9zout \u306B\u3061\u306A\u3093\u3067\u540D\u3065\u3051\u3089\u308C\u3066\u3044\u308B\u3002"@ja . . . "B\u00E9zout\u016Fv obor je v matematice, zejm\u00E9na v algeb\u0159e, ozna\u010Den\u00ED pro takov\u00FD obor integrity, ve kter\u00E9m je sou\u010Det dvou hlavn\u00EDch ide\u00E1l\u016F tak\u00E9 hlavn\u00EDm ide\u00E1lem. Z toho plyne zejm\u00E9na jednak to, \u017Ee pro ka\u017Ed\u00E9 dva prvky dan\u00E9ho oboru plat\u00ED B\u00E9zoutova rovnost, jednak \u017Ee ka\u017Ed\u00FD kone\u010Dn\u011B generovan\u00FD ide\u00E1l je tak\u00E9 hlavn\u00ED. Ka\u017Edou z t\u011Bchto podm\u00EDnek lze pou\u017E\u00EDt z\u00E1rove\u0148 jako defini\u010Dn\u00ED podm\u00EDnku B\u00E9zoutova oboru."@cs . . . . . "813142835"^^ . . . . "\u30D9\u30BA\u30FC\u6574\u57DF"@ja . "9267"^^ . "En alg\u00E8bre commutative, un anneau quasi-b\u00E9zoutien est un anneau o\u00F9 la propri\u00E9t\u00E9 de B\u00E9zout est v\u00E9rifi\u00E9e ; plus formellement, c'est un anneau dans lequel tout id\u00E9al de type fini est principal. Un anneau de B\u00E9zout, ou anneau b\u00E9zoutien, est un anneau quasi-b\u00E9zoutien int\u00E8gre."@fr . . . . "\u041A\u0456\u043B\u044C\u0446\u0435 \u0411\u0435\u0437\u0443 (\u043D\u0430\u0437\u0432\u0430\u043D\u0435 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0415\u0442\u044C\u0454\u043D\u0430 \u0411\u0435\u0437\u0443) \u2014 \u043E\u0431\u043B\u0430\u0441\u0442\u044C \u0446\u0456\u043B\u0456\u0441\u043D\u043E\u0441\u0442\u0456, \u0432 \u044F\u043A\u0456\u0439 \u043A\u043E\u0436\u0435\u043D \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E\u043F\u043E\u0440\u043E\u0436\u0434\u0435\u043D\u0438\u0439 \u0456\u0434\u0435\u0430\u043B \u0454 \u0433\u043E\u043B\u043E\u0432\u043D\u0438\u043C. \u0417 \u0446\u044C\u043E\u0433\u043E \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0432\u0438\u043F\u043B\u0438\u0432\u0430\u0454, \u0449\u043E \u043A\u0456\u043B\u044C\u0446\u0435 \u0411\u0435\u0437\u0443 \u043D\u0435\u0442\u0435\u0440\u043E\u0432\u0435 \u0442\u043E\u0434\u0456 \u0456 \u0442\u0456\u043B\u044C\u043A\u0438 \u0442\u043E\u0434\u0456, \u043A\u043E\u043B\u0438 \u0432\u043E\u043D\u043E \u0454 \u043A\u0456\u043B\u044C\u0446\u0435\u043C \u0433\u043E\u043B\u043E\u0432\u043D\u0438\u0445 \u0456\u0434\u0435\u0430\u043B\u0456\u0432, \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F\u043C \u044F\u043A\u0438\u0445 \u0456 \u0454 \u043A\u0456\u043B\u044C\u0446\u044F \u0411\u0435\u0437\u0443."@uk . . "\u041A\u043E\u043B\u044C\u0446\u043E \u0411\u0435\u0437\u0443"@ru . "Bezout ring"@en . . . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u30D9\u30BA\u30FC\u6574\u57DF (B\u00E9zout domain) \u306F2\u3064\u306E\u4E3B\u30A4\u30C7\u30A2\u30EB\u306E\u548C\u304C\u518D\u3073\u4E3B\u30A4\u30C7\u30A2\u30EB\u306B\u306A\u308B\u3088\u3046\u306A\u6574\u57DF\u3067\u3042\u308B\u3002\u3053\u306E\u3053\u3068\u304C\u610F\u5473\u3059\u308B\u306E\u306F\u3001\u5143\u306E\u5404\u7D44\u306B\u5BFE\u3057\u3066\u30D9\u30BA\u30FC\u306E\u7B49\u5F0F (B\u00E9zout identity) \u304C\u6210\u308A\u7ACB\u3061\u3001\u3059\u3079\u3066\u306E\u6709\u9650\u751F\u6210\u30A4\u30C7\u30A2\u30EB\u306F\u5358\u9805\u3067\u3042\u308B\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308B\u3002\u4EFB\u610F\u306E\u5358\u9805\u30A4\u30C7\u30A2\u30EB\u6574\u57DF (PID) \u306F\u30D9\u30BA\u30FC\u6574\u57DF\u3060\u304C\u3001\u30D9\u30BA\u30FC\u6574\u57DF\u306F\u30CD\u30FC\u30BF\u30FC\u74B0\u3068\u306F\u9650\u3089\u306A\u3044\u306E\u3067\u3001\u6709\u9650\u751F\u6210\u3067\u306A\u3044\u30A4\u30C7\u30A2\u30EB\u3092\u3082\u3064\u304B\u3082\u3057\u308C\u306A\u3044\uFF08\u3053\u308C\u306F\u660E\u3089\u304B\u306B PID \u3067\u306A\u3044\uFF09\u3002\u305D\u3046\u3067\u3042\u308C\u3070\u3001\u4E00\u610F\u5206\u89E3\u6574\u57DF (UFD) \u3067\u306F\u306A\u3044\u304C\u3001\u306A\u304AGCD\u6574\u57DF\u3067\u3042\u308B\u3002\u30D9\u30BA\u30FC\u6574\u57DF\u306E\u7406\u8AD6\u306F PID \u306E\u6027\u8CEA\u306E\u591A\u304F\u3092\u3001\u30CD\u30FC\u30BF\u30FC\u6027\u3092\u8981\u6C42\u305B\u305A\u306B\u3001\u4FDD\u3064\u3002\u30D9\u30BA\u30FC\u6574\u57DF\u306F\u30D5\u30E9\u30F3\u30B9\u4EBA\u6570\u5B66\u8005 \u00C9tienne B\u00E9zout \u306B\u3061\u306A\u3093\u3067\u540D\u3065\u3051\u3089\u308C\u3066\u3044\u308B\u3002"@ja . . . . "p/b015990"@en . . . . "B\u00E9zout\u016Fv obor"@cs . . "\u041A\u043E\u043B\u044C\u0446\u043E \u0411\u0435\u0437\u0443 (\u043D\u0430\u0437\u0432\u0430\u043D\u043D\u043E\u0435 \u043F\u043E \u0438\u043C\u0435\u043D\u0438 \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u042D\u0442\u044C\u0435\u043D\u0430 \u0411\u0435\u0437\u0443) \u2014 \u044D\u0442\u043E \u0432\u0441\u044F\u043A\u0430\u044F \u043E\u0431\u043B\u0430\u0441\u0442\u044C \u0446\u0435\u043B\u043E\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043A\u0430\u0436\u0434\u044B\u0439 \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u043F\u043E\u0440\u043E\u0436\u0434\u0451\u043D\u043D\u044B\u0439 \u0438\u0434\u0435\u0430\u043B \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0433\u043B\u0430\u0432\u043D\u044B\u043C. \u0418\u0437 \u044D\u0442\u043E\u0433\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u0441\u043B\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043E \u043A\u043E\u043B\u044C\u0446\u043E \u0411\u0435\u0437\u0443 \u043D\u0451\u0442\u0435\u0440\u043E\u0432\u043E \u0442\u043E\u0433\u0434\u0430 \u0438 \u0442\u043E\u043B\u044C\u043A\u043E \u0442\u043E\u0433\u0434\u0430, \u043A\u043E\u0433\u0434\u0430 \u043E\u043D\u043E \u043A\u043E\u043B\u044C\u0446\u043E \u0433\u043B\u0430\u0432\u043D\u044B\u0445 \u0438\u0434\u0435\u0430\u043B\u043E\u0432, \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435\u043C \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043A\u043E\u043B\u044C\u0446\u0430 \u0411\u0435\u0437\u0443 \u0438 \u044F\u0432\u043B\u044F\u044E\u0442\u0441\u044F."@ru . . "\u041A\u0456\u043B\u044C\u0446\u0435 \u0411\u0435\u0437\u0443 (\u043D\u0430\u0437\u0432\u0430\u043D\u0435 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0415\u0442\u044C\u0454\u043D\u0430 \u0411\u0435\u0437\u0443) \u2014 \u043E\u0431\u043B\u0430\u0441\u0442\u044C \u0446\u0456\u043B\u0456\u0441\u043D\u043E\u0441\u0442\u0456, \u0432 \u044F\u043A\u0456\u0439 \u043A\u043E\u0436\u0435\u043D \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u043E\u043F\u043E\u0440\u043E\u0436\u0434\u0435\u043D\u0438\u0439 \u0456\u0434\u0435\u0430\u043B \u0454 \u0433\u043E\u043B\u043E\u0432\u043D\u0438\u043C. \u0417 \u0446\u044C\u043E\u0433\u043E \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0432\u0438\u043F\u043B\u0438\u0432\u0430\u0454, \u0449\u043E \u043A\u0456\u043B\u044C\u0446\u0435 \u0411\u0435\u0437\u0443 \u043D\u0435\u0442\u0435\u0440\u043E\u0432\u0435 \u0442\u043E\u0434\u0456 \u0456 \u0442\u0456\u043B\u044C\u043A\u0438 \u0442\u043E\u0434\u0456, \u043A\u043E\u043B\u0438 \u0432\u043E\u043D\u043E \u0454 \u043A\u0456\u043B\u044C\u0446\u0435\u043C \u0433\u043E\u043B\u043E\u0432\u043D\u0438\u0445 \u0456\u0434\u0435\u0430\u043B\u0456\u0432, \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0435\u043D\u043D\u044F\u043C \u044F\u043A\u0438\u0445 \u0456 \u0454 \u043A\u0456\u043B\u044C\u0446\u044F \u0411\u0435\u0437\u0443."@uk . . "In mathematics, a B\u00E9zout domain is a form of a Pr\u00FCfer domain. It is an integral domain in which the sum of two principal ideals is again a principal ideal. This means that for every pair of elements a B\u00E9zout identity holds, and that every finitely generated ideal is principal. Any principal ideal domain (PID) is a B\u00E9zout domain, but a B\u00E9zout domain need not be a Noetherian ring, so it could have non-finitely generated ideals (which obviously excludes being a PID); if so, it is not a unique factorization domain (UFD), but still is a GCD domain. The theory of B\u00E9zout domains retains many of the properties of PIDs, without requiring the Noetherian property. B\u00E9zout domains are named after the French mathematician \u00C9tienne B\u00E9zout."@en . . . . . "\u041A\u043E\u043B\u044C\u0446\u043E \u0411\u0435\u0437\u0443 (\u043D\u0430\u0437\u0432\u0430\u043D\u043D\u043E\u0435 \u043F\u043E \u0438\u043C\u0435\u043D\u0438 \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u042D\u0442\u044C\u0435\u043D\u0430 \u0411\u0435\u0437\u0443) \u2014 \u044D\u0442\u043E \u0432\u0441\u044F\u043A\u0430\u044F \u043E\u0431\u043B\u0430\u0441\u0442\u044C \u0446\u0435\u043B\u043E\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043A\u0430\u0436\u0434\u044B\u0439 \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u043F\u043E\u0440\u043E\u0436\u0434\u0451\u043D\u043D\u044B\u0439 \u0438\u0434\u0435\u0430\u043B \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0433\u043B\u0430\u0432\u043D\u044B\u043C. \u0418\u0437 \u044D\u0442\u043E\u0433\u043E \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044F \u0441\u043B\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043E \u043A\u043E\u043B\u044C\u0446\u043E \u0411\u0435\u0437\u0443 \u043D\u0451\u0442\u0435\u0440\u043E\u0432\u043E \u0442\u043E\u0433\u0434\u0430 \u0438 \u0442\u043E\u043B\u044C\u043A\u043E \u0442\u043E\u0433\u0434\u0430, \u043A\u043E\u0433\u0434\u0430 \u043E\u043D\u043E \u043A\u043E\u043B\u044C\u0446\u043E \u0433\u043B\u0430\u0432\u043D\u044B\u0445 \u0438\u0434\u0435\u0430\u043B\u043E\u0432, \u043E\u0431\u043E\u0431\u0449\u0435\u043D\u0438\u0435\u043C \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043A\u043E\u043B\u044C\u0446\u0430 \u0411\u0435\u0437\u0443 \u0438 \u044F\u0432\u043B\u044F\u044E\u0442\u0441\u044F. \u0426\u0435\u043B\u043E\u0441\u0442\u043D\u043E\u0435 \u043A\u043E\u043B\u044C\u0446\u043E \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043A\u043E\u043B\u044C\u0446\u043E\u043C \u0411\u0435\u0437\u0443 \u0442\u043E\u0433\u0434\u0430 \u0438 \u0442\u043E\u043B\u044C\u043A\u043E \u0442\u043E\u0433\u0434\u0430, \u043A\u043E\u0433\u0434\u0430 \u0432 \u044D\u0442\u043E\u043C \u043A\u043E\u043B\u044C\u0446\u0435 \u043B\u044E\u0431\u044B\u0435 \u0434\u0432\u0430 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u0430 \u0438\u043C\u0435\u044E\u0442 \u043D\u0430\u0438\u0431\u043E\u043B\u044C\u0448\u0438\u0439 \u043E\u0431\u0449\u0438\u0439 \u0434\u0435\u043B\u0438\u0442\u0435\u043B\u044C (\u041D\u041E\u0414), \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043C\u044B\u0439 \u0432 \u0432\u0438\u0434\u0435 \u0438\u0445 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0439 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0446\u0438\u0438. (\u042D\u0442\u043E \u0443\u0441\u043B\u043E\u0432\u0438\u0435 \u043E\u0437\u043D\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043E \u043A\u0430\u0436\u0434\u044B\u0439 \u0438\u0434\u0435\u0430\u043B \u0441 \u0434\u0432\u0443\u043C\u044F \u043E\u0431\u0440\u0430\u0437\u0443\u044E\u0449\u0438\u043C\u0438 \u0434\u043E\u043F\u0443\u0441\u043A\u0430\u0435\u0442 \u043E\u0434\u043D\u0443 \u043E\u0431\u0440\u0430\u0437\u0443\u044E\u0449\u0443\u044E, \u0438\u0437 \u0447\u0435\u0433\u043E \u043F\u043E \u0438\u043D\u0434\u0443\u043A\u0446\u0438\u0438 \u0432\u044B\u0432\u043E\u0434\u0438\u0442\u0441\u044F, \u0447\u0442\u043E \u043A\u0430\u0436\u0434\u044B\u0439 \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u043F\u043E\u0440\u043E\u0436\u0434\u0451\u043D\u043D\u044B\u0439 \u0438\u0434\u0435\u0430\u043B \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0433\u043B\u0430\u0432\u043D\u044B\u043C.) \u041F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u0435 \u041D\u041E\u0414\u0430 \u0434\u0432\u0443\u0445 \u044D\u043B\u0435\u043C\u0435\u043D\u0442\u043E\u0432 \u0438\u0445 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0439 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0446\u0438\u0435\u0439 \u0447\u0430\u0441\u0442\u043E \u043D\u0430\u0437\u044B\u0432\u0430\u044E\u0442 \u0442\u043E\u0436\u0434\u0435\u0441\u0442\u0432\u043E\u043C \u0411\u0435\u0437\u0443."@ru . "\uAC00\uD658\uB300\uC218\uD559\uC5D0\uC11C \uBCA0\uC8FC \uC815\uC5ED(B\u00E9zout\u6574\u57DF, \uC601\uC5B4: B\u00E9zout domain)\uC740 \uBCA0\uC8FC \uD56D\uB4F1\uC2DD\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uC815\uC5ED\uC774\uB2E4."@ko . . "In mathematics, a B\u00E9zout domain is a form of a Pr\u00FCfer domain. It is an integral domain in which the sum of two principal ideals is again a principal ideal. This means that for every pair of elements a B\u00E9zout identity holds, and that every finitely generated ideal is principal. Any principal ideal domain (PID) is a B\u00E9zout domain, but a B\u00E9zout domain need not be a Noetherian ring, so it could have non-finitely generated ideals (which obviously excludes being a PID); if so, it is not a unique factorization domain (UFD), but still is a GCD domain. The theory of B\u00E9zout domains retains many of the properties of PIDs, without requiring the Noetherian property. B\u00E9zout domains are named after the French mathematician \u00C9tienne B\u00E9zout."@en . . . . . "\u041A\u0456\u043B\u044C\u0446\u0435 \u0411\u0435\u0437\u0443"@uk . . . "Nella teoria degli anelli, un dominio di B\u00E9zout \u00E8 una forma di dominio di Pr\u00FCfer. \u00C8 un dominio d'integrit\u00E0 in cui la somma di due ideali principali \u00E8 ancora un ideale principale. Questo significa che un'identit\u00E0 di B\u00E9zout vale per ogni coppia di elementi, e che ogni ideale finitamente generato \u00E8 principale. Ogni dominio ad ideali principali (PID) \u00E8 un dominio di B\u00E9zout, ma non \u00E8 necessario che quest'ultimo sia un anello noetheriano, quindi potrebbe avere degli ideali non finitamente generati (che ovviamente esclude dall'essere un PID); se \u00E8 cos\u00EC, allora non \u00E8 un dominio a fattorizzazione unica (UFD), ma rimane un dominio MCD (cio\u00E8 ogni coppia di elementi ha un massimo comun divisore). La teoria dei domini di B\u00E9zout conserva molte propriet\u00E0 dei PID, senza richiedere la propriet\u00E0 noetheriana"@it . "En alg\u00E8bre commutative, un anneau quasi-b\u00E9zoutien est un anneau o\u00F9 la propri\u00E9t\u00E9 de B\u00E9zout est v\u00E9rifi\u00E9e ; plus formellement, c'est un anneau dans lequel tout id\u00E9al de type fini est principal. Un anneau de B\u00E9zout, ou anneau b\u00E9zoutien, est un anneau quasi-b\u00E9zoutien int\u00E8gre."@fr . . . . . . . . . "Nella teoria degli anelli, un dominio di B\u00E9zout \u00E8 una forma di dominio di Pr\u00FCfer. \u00C8 un dominio d'integrit\u00E0 in cui la somma di due ideali principali \u00E8 ancora un ideale principale. Questo significa che un'identit\u00E0 di B\u00E9zout vale per ogni coppia di elementi, e che ogni ideale finitamente generato \u00E8 principale. Ogni dominio ad ideali principali (PID) \u00E8 un dominio di B\u00E9zout, ma non \u00E8 necessario che quest'ultimo sia un anello noetheriano, quindi potrebbe avere degli ideali non finitamente generati (che ovviamente esclude dall'essere un PID); se \u00E8 cos\u00EC, allora non \u00E8 un dominio a fattorizzazione unica (UFD), ma rimane un dominio MCD (cio\u00E8 ogni coppia di elementi ha un massimo comun divisore). La teoria dei domini di B\u00E9zout conserva molte propriet\u00E0 dei PID, senza richiedere la propriet\u00E0 noetheriana. I domini di B\u00E9zout devono il loro nome dal matematico francese \u00C9tienne B\u00E9zout."@it . "Anneau de B\u00E9zout"@fr . "\uBCA0\uC8FC \uC815\uC5ED"@ko . . "B\u00E9zout\u016Fv obor je v matematice, zejm\u00E9na v algeb\u0159e, ozna\u010Den\u00ED pro takov\u00FD obor integrity, ve kter\u00E9m je sou\u010Det dvou hlavn\u00EDch ide\u00E1l\u016F tak\u00E9 hlavn\u00EDm ide\u00E1lem. Z toho plyne zejm\u00E9na jednak to, \u017Ee pro ka\u017Ed\u00E9 dva prvky dan\u00E9ho oboru plat\u00ED B\u00E9zoutova rovnost, jednak \u017Ee ka\u017Ed\u00FD kone\u010Dn\u011B generovan\u00FD ide\u00E1l je tak\u00E9 hlavn\u00ED. Ka\u017Edou z t\u011Bchto podm\u00EDnek lze pou\u017E\u00EDt z\u00E1rove\u0148 jako defini\u010Dn\u00ED podm\u00EDnku B\u00E9zoutova oboru."@cs . . . . . . . . . . "Dominio di B\u00E9zout"@it . .