I know an ideal in a ring is a module over this ring, but I don't know why it's a submodule of a free module, what's the free module? Thank you.
2026-04-02 19:42:44.1775158964
Why an ideal in a ring is a submodule of a free module over that ring
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A fintely generated free $R$-module is isomorphic to $R^n$. Take $n=1$ and you see that $R$ is a free $R$-module. Now it is left to check that an ideal $I\subset R$ defines an $R$-submodule. But this is clear by definition. Is every step and the result clear to you?