Here $\mathfrak a$ is an ideal of a commutative ring $A$. Show that $\mathfrak a$ is principal if it is free as an $A$-module.
2026-04-25 04:16:47.1777090607
Show that if an ideal is free as a module then it is principal.
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Hint: The key is to show that an ideal which is free as an $A$-module is free of rank at most $1$. To see this it is enough to show that no ideal of $A$ contains two $A$-linearly independent elements.