M is an R-module, where M is a commutative ring, if $M≅R/I$ for some ideal I of R, then show $M$ is a cyclic R-module.
Note: $M$ is a cyclic R-module means $M=<m>$ for some $m\in M$.
Please help, I have not idea how to do this, thanks a lot!
2026-04-01 08:52:08.1775033528
M an R-module, where M is a commutative ring, if $M≅R/I$ for some ideal I of R, then $M$ is a cyclic R-module
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$R/I$ is generated by the class of $1$. (If $R$ is not unitary, the assertion is false anyway)