I have a question about rings of global dimension one.
I read that these rings are hereditary rings, that is, every right ideal is projective.
How can I prove this fact ?
Thanks a lot :)
2026-03-25 02:57:24.1774407444
Global Dimension 1
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A ring $R$ is (left) hereditary if and only if all (left) modules have projective resolutions of length at most $1$. But this is by definition equivalent to saying that the (left) global dimension is at most $1$.