Jon O.
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 Dec 16 awarded Caucus Sep 24 awarded Critic Nov 20 awarded Nice Question Jul 10 comment Is $U=\{(r,s,t)|r,s,t \in \mathbb{R}, -r+3s+2t=0\}$ a subspace of $\mathbb{R}^3$? Let $u = (r_1, s_1, t_1)$ and $v = (r_2, s_2, t_2)$ be any two elements of $U$, and $a$ be any real number. If you write out the sum $u + v$ and the product $au$ in terms of the coordinates $r_1, r_2, ...$, can you check whether they satisfy the equation defining $U$? Jun 17 awarded Enthusiast Jun 13 accepted A simpler proof that if $m\mid n$ then there is a ring homomorphism from $\mathbb{Z}_n$ onto $\mathbb{Z}_m$? Jun 13 comment A simpler proof that if $m\mid n$ then there is a ring homomorphism from $\mathbb{Z}_n$ onto $\mathbb{Z}_m$? Thanks for this answer. Yes, I have often guilty of jumping the gun in this respect, but in this case I really have the details in mind. ;-) It seems to me that the coset notation makes it easier to distinguish integers, residue classes $\pmod{n}$ and residue classes $\pmod{m}$, but I think I can see now how to rephrase the argument in terms of residue classes if I had to. Jun 12 comment A simpler proof that if $m\mid n$ then there is a ring homomorphism from $\mathbb{Z}_n$ onto $\mathbb{Z}_m$? @ThomasAndrews: Ha, point taken. I still wonder what kind of answer the author expects the student to be able to give at this point, but I guess I will be content to treat $\mathbb{Z}/(m)$ as the definition of $\mathbb{Z}_m$ and not worry further about it. ;-) Jun 12 asked A simpler proof that if $m\mid n$ then there is a ring homomorphism from $\mathbb{Z}_n$ onto $\mathbb{Z}_m$? Jun 12 comment Must an ideal contain the kernel for its image to be an ideal? Thank you for the followup. Jun 12 comment Must an ideal contain the kernel for its image to be an ideal? Thank you for the additional hint. Jun 10 awarded Editor Jun 10 awarded Scholar Jun 10 revised Must an ideal contain the kernel for its image to be an ideal? Edit title so as not to be misleading Jun 10 accepted Must an ideal contain the kernel for its image to be an ideal? Jun 10 comment Must an ideal contain the kernel for its image to be an ideal? Aha, fantastic! It almost seems to me like there is an extra part missing from the problem. The next question asks to prove that if $f$ is onto and $B$ is a field then $ker f$ is a maximal ideal, and you would need the reverse direction to show that (if I understand correctly). Jun 10 awarded Student Jun 10 asked Must an ideal contain the kernel for its image to be an ideal? Mar 28 awarded Supporter