can somebody please explain how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$??
2026-03-31 15:17:52.1774970272
how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$?
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A free resolution is given by $$ \dots \xrightarrow 2 \mathbb Z /4\xrightarrow 2 \mathbb Z/4\xrightarrow 2 \mathbb Z/4 \rightarrow \mathbb Z/2, $$ where the last map is enlargement of cosets and, by a standard abuse of notation, $2$ denotes the map $\bar 1\mapsto \bar 2$ (where bar denotes residue class). See the answer to this question.