Why $I$ is a proper ideal implies $1\notin I$?
The definition of proper ideal only requires $I\neq R$. I don't get it.
2026-03-30 02:10:29.1774836629
Why proper ideal doesn't contain $1$?
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For an ideal $I$, if $a\in I$ and $r\in R$, then $ra\in I$. So, if $1\in I$ then $r=r1\in I$ for all $r\in R$; therefore $I=R$.