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0400U000239,
к.ф.-м.н.
24-01-2000
o
Rings of elementary divisors and related algebraic structures
Romaniv Oleg Mykolajovych,
popup.head Забавський Богдан Володимирович
popup.opponent Рябухін Юрій Михайлович
popup.opponent Дубровін Микола Іванович
Дисертацiю присвячено дослiдженню кілець елементарних дільників, а точніше їх частковому випадку - кілець з елементарною редукцією матриць. Знайдено нові класи як комутативниx, так і некомутативних кілець з елементарною редукцією матриць. Встановлено властивості некомутативних елементарно головних кілець, однобічних w-евклідових кілець з їх подальшим дослідженням на предмет можливості елементарної редукції матриць. Досліджено кільця Безу і 2-евклідові кільця, в яких довільний максимально неголовний правий ідеал є двобічним, і описано в даному класі кільця, над якими можлива елементарна редукція матриць. Ключовi слова: кільце Безу, кільце елементарних дільників, кільце з елементарною редукцією матриць, дуо-кільце, максимально неголовний правий ідеал.
2000-01-24
2020-04-04
Updated: 2025-12-07
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