Алгебра | Константин Чепуркин. Лекция 4

1:25:30 Обратный элемент (a+b√2)^-1=(a−b√2)/(a^2−2b^2).
1:32:30 Ещё выполняется f(x^-1)=f(x)^-1. Потому что 1'=f(1)=f(xx^-1)=f(x)f(x^-1) ⇒ f(x)^-1=f(x^-1). Плюс для гоморфирзмов групп можно сказать, что H=f^-1(1) − подгруппа H⊂G. Если f из группы G1 действует в группу G2, то H=f(G1) будет подгруппой H⊂G2, тоже самое верно для колец.

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