23h
awarded Enlightened
23h
awarded Nice Answer
Jan
14
comment Congratulations (again), Daniel Fischer!
I understand. Let's consolidate these posts in one place. :)
Jan
14
comment Congratulations (again), Daniel Fischer!
We already have a congratulatory post for Daniel here. Voting as duplicate.
Jan
11
comment Is $\phi: C^{\infty}(\mathbb{R}) \to (\mathbb{R},+), \phi(f) = f'(0)$ an isomorphism?
Thank you! ${}$
Jan
11
comment Is $\phi: C^{\infty}(\mathbb{R}) \to (\mathbb{R},+), \phi(f) = f'(0)$ an isomorphism?
Could you please give your questions better titles? This is your third question with the title "is this an isomorphism?".
Jan
10
comment Prove that factor rings are fields
Please search the site before posting. There already are many variations of this question.
Jan
10
comment Show that $(A / \mathfrak{a}) \otimes_A M \cong M / \mathfrak{a} M$ for a ring $A$, ideal $\mathfrak{a}$, $A$-module $M$.
It's a different presentation of the same argument. It might be more accessible to some. I actually added this to the comments when the question was posted. Since other proofs were posted, I didn't want my comments to be lost.
Jan
9
answered Show that $(A / \mathfrak{a}) \otimes_A M \cong M / \mathfrak{a} M$ for a ring $A$, ideal $\mathfrak{a}$, $A$-module $M$.
Jan
7
comment Show that $(A / \mathfrak{a}) \otimes_A M \cong M / \mathfrak{a} M$ for a ring $A$, ideal $\mathfrak{a}$, $A$-module $M$.
The isomorphism $M \cong A\otimes_A M$ and the exact sequence $\mathfrak a \otimes_A M \to A \otimes_A M \to A/\mathfrak a \otimes_A M \to 0$ when put together give the exact sequence $\mathfrak a \otimes_A M \xrightarrow{\varphi} M \xrightarrow{\psi} A/\mathfrak a \otimes_A M \to 0$. Since $\ker \psi = \im \varphi = \mathfrak aM$, the first isomorphism theorem gives the desired result.
Jan
7
comment Show that $(A / \mathfrak{a}) \otimes_A M \cong M / \mathfrak{a} M$ for a ring $A$, ideal $\mathfrak{a}$, $A$-module $M$.
I know you're looking for proof verification, but this proof is very long and technical. You can finish the proof quickly by using the isomorphism $M \cong M \otimes_A A$ and the exact sequence you have at the beginning.
Jan
3
awarded Popular Question
Jan
3
comment Is the question in the Munkres's topology book wrong?
The definition of $[I, Y]$ does not require end points to be fixed, unlike the case with the fundamental group. This is a crucial difference.
Jan
2
comment Need help on how to compute the fundamental group of a space.
You can realize this space as a CW-complex by attaching one $2$-cell to a wedge sum of $5$ circles. The attaching map can be inferred from the diagram. This is one way to compute the fundamental group.
Dec
25
comment A question about the geometric representation of Spec $\Bbb{C}[x,y]/(x-y)$
It might be easier to see the correspondence via the isomorphism $\mathbb C[x, y]/(x-y) \cong \mathbb C[x]$.
Dec
23
comment What is going on with undeletion lately?
I agree that answering PSQs is often driven by reputation. However, I have an observation to make. Most votes on PSQs happen early on during the question's life cycle. Reputation already earned isn't taken back when the question is converted to CW. I don't think that flagging and manual conversion to CW would be quick enough. Answering PSQ would remain an effective way for harvesting reputation.
Dec
23
comment What is going on with undeletion lately?
@Brian Definitely, examples are crucial for good understanding. This is why a canonical answer should contain some examples in addition to the general theory. Here is a canonical answer on integration by partial fractions; it contains plenty of examples. I think students would learn a lot more if they were referred to this question, as opposed to seeing their particular exercise solved for them. Alas, some of our 10K+ are willing to answer hundreds of such questions, adding very little value to the site, and burying good questions in the process.
Dec
22
comment What is going on with undeletion lately?
@NajibIdrissi The point is, 10K+ users should know better than to answer yet another quadratic equation question. We already have excellent answers explaining the general method. Adding an answer, and reopening/undeleting the question (potentially to preserve reputation) is not a positive contribution to the site.
Dec
22
comment What is going on with undeletion lately?
@NajibIdrissi And the undeletions happened by the same group of three. I don't know if this counts as some sort of conflict of interest.
Dec
22
comment What is going on with undeletion lately?
Such questions should be closed as abstract duplicates of answers that explain the general method. We cannot afford to have a question with specific solutions for every quadratic equation out there. Such questions add zero value to the site and make it more difficult to find interesting questions. That said, we have no such consensus in the community, and some users want to continue to answer such zero value questions and undelete them when they get deleted.
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