> knowing that a ring is “like a group...” is useful
Turns out, not so much, though. The ring theory bears surprisingly little resemblance to the group theory, to the point that these concepts seem to have nothing to do with each other...
Turns out, not so much, though. The ring theory bears surprisingly little resemblance to the group theory, to the point that these concepts seem to have nothing to do with each other...
Do you seriously mean to suggest there's no pedagogical value in using groups to teach rings?
Otherwise I agree with you, there's a lot of pedagogical value in combining coverage of algebraic structures.