What's being called the second Isomorphism theorem for modules looks more like the third isomorphism theorem for groups, and vice versa.
MA3G6 Commutative Algebra Page 8 lecture notes isomorphism theorem
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As I said when these theorems came up in the lectures, no-one agrees on the numbering but you should not worry about it. If you need to use the result, you are hereby officially allowed by me to say "by the n'th isomorphism theorem" with any value of n (including a symbolic "n"), and as long as you quote and use the result correctly, that's ok. In Atiyah-Macdonald the results I called the Second and Third I.T.s are just two parts of a rpoposition with no special names. It's not important!0 likes
Thanks :)0 likes