Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1304-2461-9 |
Объём: | 64 страниц |
Масса: | 117 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! The maps between the kernels and the maps between the cokernels are induced in a natural manner by the given maps because of the diagram's commutativity. The exactness of the two induced sequences follows in a straightforward way from the exactness of the rows of the original diagram. The important statement of the lemma is that a connecting homomorphism d exists which completes the exact sequence. In the case of abelian groups or modules over some ring, the map d can be constructed as follows. Pick an element x in ker c and view it as an element of C; since g is surjective, there exists y in B with g(y) = x. Because of the commutativity of the diagram, we have g'(b(y)) = c(g(y)) = c(x) = 0 (since x is in the kernel of c), and therefore b(y) is in the kernel of g' . Since the bottom row is exact, we find an element z in A' with f '(z) = b(y). We then define d(x) = z + im(a). Now one has to check that d is well-defined.
Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.