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seen Dec 16 at 2:46

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