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Apr
19
comment Is there any notion of “smoothification” from $\mathbb{R}$-schemes to generalized smooth spaces?
I would think the obvious thing would be to send a finite type affine scheme to its set of real points as a subset of $\mathbb{R}^n$ (with the induced smooth structure), and then to extend to arbitrary schemes by taking colimits.
Apr
16
comment Structure theorem for infinitely generated modules over a PID
@Ycor: That's correct. For details, see the second paragraph of my answer here.
Apr
11
awarded  Popular Question
Apr
11
answered Projective resolutions of torsion modules
Mar
31
awarded  Notable Question
Mar
29
answered What does the notation $[b_1,b_2]$ in M. Hochster's “Prime Ideal Structure in Commutative Rings” mean?
Mar
28
revised What does the notation $[b_1,b_2]$ in M. Hochster's “Prime Ideal Structure in Commutative Rings” mean?
more direct link
Mar
28
comment What does the notation $[b_1,b_2]$ in M. Hochster's “Prime Ideal Structure in Commutative Rings” mean?
Not sure how this is off-topic...I just took another look at the paper myself and am puzzling over what the notation is supposed to mean. I can't tell for sure, but I think it is supposed to denote the subring generated by $b_1$ and $b_2$.
Mar
26
awarded  Nice Answer
Feb
28
awarded  Deputy
Feb
20
awarded  Nice Answer
Feb
19
awarded  Enlightened
Feb
19
awarded  Nice Answer
Feb
19
answered Does the functor Sch to Top have a right adjoint?
Feb
11
awarded  Enlightened
Feb
5
comment About equalizer of Boolean algebras
No, they aren't the same in general. For instance, let $I$ be any connected compact Hausdorff space, and let $\pi:S\to I$ be any continuous surjection from a Stone space to $I$. Taking the kernel pair of $\pi$ gives a pair of maps $\varphi^*,\psi^*:T\to S$ from some Stone space $T$ whose coequalizer is $\pi$. Thus the quotient by the equivalence relation $\sim'$ in this case is $I$. But the quotient by $\sim$ will be just a point, since $I$ is connected.
Feb
3
answered About equalizer of Boolean algebras
Feb
1
awarded  Enlightened
Feb
1
awarded  Nice Answer
Feb
1
answered Description of $\big(\ell^\infty(\mathbb N)\big)^{\!*}$ via ultrafilters