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Borderline surprised this is on the frontpage. :)

Here are two comments from yours truly on what "ideals" are and why they make sense to think about for number theory:

Ah yes, but it is the generalisation to _fractional_ ideals that is required to obtain the ideal class group.

I know, but it's good to understand the _trivial_ fractional ideals first. :)

(I like your blog, btw!)

Thanks for the kind remarks :-)