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Dec 1, 2016 at 15:19 comment added R. Morty Ah yes sloppy notation on my part. Thanks again!
Dec 1, 2016 at 14:50 comment added Pace Nielsen Basically, yes, except that $R/I$ is only isomorphic (not equal) to a submodule of $R$.
Dec 1, 2016 at 14:44 vote accept R. Morty
Dec 1, 2016 at 14:44 comment added R. Morty Ok I think I got it thanks. To get used to the different notations, basically $R/I$ projective means $(1)=R=R/I \oplus I=(1+I)\oplus I$ so $I$ cyclic as well?
Dec 1, 2016 at 14:04 history answered Pace Nielsen CC BY-SA 3.0