Algebraic Topology · Problem 3.1.3

Cohomology — Allen Hatcher

Mathematics — Topology · ext-over-z4

Problem

Regarding Z2\mathbb{Z}_2 as a module over the ring Z4\mathbb{Z}_4, construct a resolution of Z2\mathbb{Z}_2 by free modules over Z4\mathbb{Z}_4 and use this to show that ExtZ4n(Z2,Z2)\text{Ext}^n_{\mathbb{Z}_4}(\mathbb{Z}_2, \mathbb{Z}_2) is nonzero for all nn.

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