MATRITSA DETERMINANTLARI VA ULARNING ALGEBRAIK STRUKTURALARDAGI QO‘LLANILISHLARI
Keywords:
determinant, algebraik struktura, kommutativ halqa, maydon, modul, minor, Smith normal shakli, determinantal ideal, Fitting invariantiAbstract
Ushbu maqolada matritsa determinantlari nazariyasining asosiy mazmuni, determinantning algebraik tabiati hamda uning turli algebraik strukturalardagi qo‘llanilishlari tahlil qilinadi. Determinantning ko‘p chiziqlilik, alternirlovchanlik, normallashganlik va multiplikativlik kabi fundamental xossalari izchil bayon qilinib, ularning chiziqli tenglamalar sistemasi, teskari matritsa, xarakteristik ko‘phad, kommutativ halqalar va modullar nazariyasidagi o‘rni yoritiladi. Shuningdek, determinantning Smith normal shakli, determinantal ideallar va Fitting invariantlari bilan bog‘liqligi ko‘rsatilib, determinantning zamonaviy algebraik tadqiqotlardagi nazariy ahamiyati asoslanadi.
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