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...
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.
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Классический текст по теории медиа, книга "Понимание медиа" канадского философа, филолога и культуролога Маршалла Герберта Маклюэна (1911-1980), вышла в 1964 году, на двадцать лет предвосхитив появление персонального компьютера и на тридцать - распространение Интернета. Термин "глобальная деревня" и тезис "средство коммуникации есть сообщение" получили самое широкое распространение в науке, литературе и...
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Кучково поле
Дата выхода: декабрь 2018
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