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The Venerable Samuel Handwich, Scholar.


2d
accepted Where was I supposed to use compactness in this proof that a compact subspace can be separated from a point by open sets?
2d
comment Where was I supposed to use compactness in this proof that a compact subspace can be separated from a point by open sets?
@DanielCooney Sorry, that was a vestigal part from when I had originally tried to use a finite subcover. But then I realized I didn't need it for this argument to work. I repaired it above.
2d
revised Where was I supposed to use compactness in this proof that a compact subspace can be separated from a point by open sets?
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2d
asked Where was I supposed to use compactness in this proof that a compact subspace can be separated from a point by open sets?
Jul
2
awarded  Curious
Apr
25
awarded  Quorum
Apr
4
revised Orthogonal idempotents from disjoint union in $\text{Spec}(A)$
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Apr
4
revised Non-cyclic finite extensions of fixed fields of infinite order automorphisms of non-algebraically closed fields
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Apr
4
accepted Reference request: Introduction to Finite Group Cohomology
Apr
4
asked Example of $\sum_i a_i\otimes b_i\in M\otimes_AN$ which cannot be written as $a\otimes b$
Mar
30
asked Galois group of $x^5-12x+2$ over $\mathbb{Q}$
Mar
30
asked Did the world experience a “mathematical drought” at any time in history?
Mar
30
accepted Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
revised Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
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Mar
29
comment Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
So, what do I do from here...? (This isn't homework, I'm just stuck, my ring theory sucks.)
Mar
29
asked Groups of order $p^aq^br^c$ containing elements of order $pq$, $qr$, and $pr$, but not $pqr$
Mar
29
comment Explicitly computing the isomorphism class of the tensor product of two finite abelian groups
I'm mimicing Servaes' solution to show what you suggested about $\mathbb{Z}_{p^e}\otimes_\mathbb{Z}\mathbb{Z}_{q^f}$. If $p\ne q$, $q^f$ is invertible in $\mathbb{Z}_{p^e}$, so $$a\otimes b=(q^{-f}q^f)a\otimes b=(q^{-f}a)\otimes (q^fb)=(q^{-f}a)\otimes 0=0$$ Check. Now I form $\xi:\mathbb{Z}_p^e\times \mathbb{Z}_p^f\rightarrow \mathbb{Z}_{p^{\min{e,f}}}$, $\phi:(a,b)\mapsto ab$. But I don't understand how to proceed from here. I also don't understand how this map tells me something about the tensor product; it's from the direct. Confused.