for the warm-up exercise at 10:54, when Michael says "where m and n are different" m and n are understood to be non-negative integers (because of course e.g. 3 *Z* and (-3) *Z* are isomorphic as rings since they are equal)
schweinmachtbree
Thanks alot, this course has been super helpful, especially all the worked examples.
neshirst-ashuach
This lecture series is absolutely brilliant. Thank you so much for sharing these with us.
music_lyrics-niks
25:00 This follows immediately from the corresponding lemma for group homomorphisms, doesn't it?! (see 11:30 in the video "First Isomorphism Theorem of Groups -- Abstract Algebra 14") One does not need any of the actual ring structure of R here, only the fact that is an additive group and that phi is a _group_ homomorphism.
bjornfeuerbacher
@38:26 who is this the kernel. Certainly it’s in the kernel, but why can’t the kernel contain more?
The characteristic is just the smallest such n, there may be greater multiples that always lead to 0?
