TEOREMAI ASOSII ALGEBRA

TEOREMAI ASOSII ALGEBRA, nomi teoremaest, ki mavjudiyati reshahoi kompleksii muodilai algebravii koeffisienthoyash kompleksii

sobit mekunad. Tarifi teorema: har guna bisyoruzvai koeffisienthoyash dilkhohi darajaash kalon yo barobari yak loaqal yak resha (dar holati umumi reshai kompleksi) dorad. In teorema yake az komyobihoi buzurgi tamomi matamatika buda, dar sohahoi mukhtalifi ilm istifoda meshavad. Masalan, tamomi nazariyai bisyoruzvahoi koeffisienthoyashon adadi ba in teorema asos meyobad. Az hamin sabab onro «teoremai asosii algebra» nomidaand. Dar asl boshad, teoremai asosii algebra teoremai sof algebravi nest. Zero baroi isboti on ba istiloh khosiyathoi topologii adadhoi haqiqi va komleksi (yane khosiyathoe, ki ba befosilagi vobastaand) istifoda shudaand. In teoremaro bori avval dar okhiri asri 17 matematiki fransavi A. Jirar bayon karda bud. Soli 1799 boshad onro K. Gauss purra isbot kardaast.

Agar yake az reshahoi muodilai algebravii (*) boshad, be dushvori isbot kardan mumkin ast, ki bisyoruzvai tarafi chapi muodila ba  be baqiya taqsim meshavad. Teoremai asosii algebraro istifoda burda ba osoni isbot kardan mumkin ast, ki har guna bisyoruzvai darajai n ba n-to zarbshavandahoi darajai yakum judo meshavad, yane:

In usul baroi bisyoruzvai dodashuda yagona ast.

Hamin tariq, muodilai darajai n-um n-to resha dorad. Dar holati khususi baze zarbshavandaho ba hamdigar barobar shudanashon mumkin ast, yane baze reshaho chand bor takror meshavand (reshahoi karati), az hamin sabab miqdori reshahoi gunogun nisbat ba darajai muodila kam shudanash ham az ehtimol dur nest.

a. Qurbonov.