Galua nazariyasi — bir noma’lumli algebraik tenglamalar, ya’ni x»+ +a^-‘+A2x»:!+a11_1x+A11=(0)…(1) ko’rinishidagi tenglamalar nazariyasi. E. Galua yaratgan. G.n ga ko’ra, (1) tenglamaning ildizlari uning AG A2,…, AP koeffisientlari orqali to’rt arifmetik amal hamda ildizdan chiqarish amali yordamida ifoda etilishi kerak. Shuning uchun ko’pincha bunday masala (1) tenglamaning radikallarda echilishi haqidagi masala deb ataladi. p=1 va i =2 bo’lgan hollar uchun bu masalaning echimi qadimdan ma’lum. p=3 va p\u20144 uchun masala uyg’onish davri (16-a.) ita — Lyan matematiklari Bombelli, Ferro, Kardano, Tartalya, Ferrari tomonidan echilgan. Keyingi uch asr mobaynida (1) tenglamani i =5 uchun radikallarda echish borasidagi urinishlar natija bermadi. Nihoyat, 1824 y.da norveg matematigi N. G. Abel p -5 bo’lganda (demak, har qanday p>5 bo’lganda ham) umuman (1) tenglamani radikallarda echib bo’lmasligini isbot qildi. Shundan keyin biror aniq (1) ko’rinishdagi tenglamani radikallarda echishning zarur va etarli shartlari qanday, degan va shunga o’xshash masalalar kelib chiqa boshladi. G.n. bu xil masalalarni bunday hal qiladi: har bir tenglamaga shu tenglama ildizlarining ba’zi chekli o’rniga qo’yishlari gruppasi taqqoslab ko’riladi (bu gruppa (1) tenglamaning Galua gruppasi deyiladi). Endi bu gruppada ba’zi xossalar (gruppaning echimiga egaligi) bajarilgan yoki bajarilmaganligi tekshiriladi. G.n. mat.ning boshqa masalalariga ham tatbiq qilinadi.<\/p>\n","protected":false},"excerpt":{"rendered":"
Galua nazariyasi — bir noma’lumli algebraik tenglamalar, ya’ni x»+ +a^-‘+A2x»:!+a11_1x+A11=(0)…(1) ko’rinishidagi tenglamalar nazariyasi. E. Galua yaratgan. G.n ga ko’ra, (1) tenglamaning ildizlari uning AG A2,…, AP koeffisientlari orqali to’rt arifmetik … Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":99837,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[210],"tags":[],"class_list":["post-132224","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-g-harfi-2","entry"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"ru","enabled_languages":["uz","kr","ru"],"languages":{"uz":{"title":true,"content":true,"excerpt":false},"kr":{"title":false,"content":false,"excerpt":false},"ru":{"title":false,"content":false,"excerpt":false}}},"_links":{"self":[{"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/posts\/132224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/comments?post=132224"}],"version-history":[{"count":1,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/posts\/132224\/revisions"}],"predecessor-version":[{"id":132235,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/posts\/132224\/revisions\/132235"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/media\/99837"}],"wp:attachment":[{"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/media?parent=132224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/categories?post=132224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/milliycha.uz\/ru\/wp-json\/wp\/v2\/tags?post=132224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}