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Консультация № 172787
30.09.2009, 22:37
25.00 руб.
0
1
1
Доброе время суток, уважаемые эксперты!
Необходима Ваша помощь в решении задач по дискретке.
Будет ли множество Z целых чисел подгруппой аддитивной группы, или идеалом в кольце А целых гауссовых чисел, т.е. чисел вида а + bi с целыми a и b ?
Заранее благодарен за ответы!
Необходима Ваша помощь в решении задач по дискретке.
Будет ли множество Z целых чисел подгруппой аддитивной группы, или идеалом в кольце А целых гауссовых чисел, т.е. чисел вида а + bi с целыми a и b ?
Заранее благодарен за ответы!
Обсуждение
Неизвестный
01.10.2009, 01:29
общий
это ответ
Здравствуйте, Николай Владимирович / Н.В..
Будет подгруппой, но не идеалом.
Подгруппой: 1. так как сумма целых чисел - целое число; 2. число, противоположное целому, - также целое.
Не идеал, так как произведение целого числа на гауссово число, вообще говоря, будет гауссовым числом. Например, 2 * (1 + i) = 2 + 2i.
Будет подгруппой, но не идеалом.
Подгруппой: 1. так как сумма целых чисел - целое число; 2. число, противоположное целому, - также целое.
Не идеал, так как произведение целого числа на гауссово число, вообще говоря, будет гауссовым числом. Например, 2 * (1 + i) = 2 + 2i.
5
Спасибо!
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