Prove Theorem 44.19 by means of the following steps. a. Show (image i *k ) (kernel
Question:
Prove Theorem 44.19 by means of the following steps.
a. Show (image i*k) ⊆ (kernel j*k).
b. Show (kernel j*k) ⊆ (image i*k).
c. Show (image j*k) ⊆ (kernel a*k).
d. Show (kernel a*k) ⊆ (image j*k).
e. Show (image a*k) ⊆ (kernel i*k-1).
f. Show (kernel i*k-1) ⊆ (image a*k).
Data from Theorem 44.19
The groups and maps of the chain complex in diagram (1) form an exact sequence.
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a We must show that j k i k 0 Let h 0 H k A Then h z B k A for some z Ak and i k h z B k A and j k z ...View the full answer
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