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585192
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location Buenos Aires, Argentina
age 21
visits member for 3 years
seen 4 hours ago

7h
answered How to prove $L_{f}(P) \leq L_{f}(Q)$ when $Q$ and $P$ are partitions of $[a,b]$ and $Q \supseteq P$
11h
comment What is your “go-to” method/style to prove convergence or divergence?
Sadly there is not one. For example, the convergence of $\sum n^{-1}\sin n$ is related to the irrationality measure of $\pi$. Series can encode deep and relevant information, and hence there is no hope for a general theorem that covers them all.
14h
comment $\gcd(4n+1, n+2)$ is found in what sense?
The Eulclidean algorithm works for any pair integers, not only the nonnegative ones. Thus, it is irrelevant whether $n\geqslant 5$ or not.
14h
comment Degrees of irreducible complex characters of alternating groups
@GeoffRobinson Given you're an active MO user, do you think this will fit there? I am doubting it.
14h
comment Is $\text{Hom}(\prod_p \Bbb Z/p\Bbb Z, \Bbb Q) = 0$ possible without choice?
(Note the argument shows more generally that in ZFC any abelian group $G$ with an element of infinite order has ${\rm Hom}(G,\Bbb Q)\neq 0$)
15h
comment Prove that $a+ib$ is prime in $\Bbb Z[i]$, of $a^2+b^2$ is prime in $\Bbb Z$.
Bill, I think readability will improve for the uninitiated if you included some words in the proof that $h$ is onto. I think the kernel part is clearer. One can obtain the same result using normal forms -- see my answer.
15h
revised Prove that $a+ib$ is prime in $\Bbb Z[i]$, of $a^2+b^2$ is prime in $\Bbb Z$.
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16h
comment Is $R$ PID if every submodule of a free $R$-module is free?
@RickyDemer Dominios de ideales principales. =)
17h
comment Find up to isomorphism all the quotient groups of composition series of a group of order $30$.
@DerekHolt I think the OP is talking about the composition factors of a composition series. Perhaps the OP is asking the determine such composition factors.
17h
answered Prove that $a+ib$ is prime in $\Bbb Z[i]$, of $a^2+b^2$ is prime in $\Bbb Z$.
1d
comment Rings in which every maximal ideal is a direct sum of cyclic modules
Please make your title more informative.
1d
revised Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
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1d
comment Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
@donnaIceberg I encourage you accept you answer, since what you did is correct. My answer should stay just as a long comment on how you can keep track of things using matrices and reading things horizontally rather than vertically.
1d
revised Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
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1d
comment Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
@donnaIceberg Your proof is correct. I have arrived at the same results as you did. Kudos!
1d
comment Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
@donnaIceberg I am not saying your algorithm is incorrect. I have edited my post.
1d
revised Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
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1d
comment Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
@donnaIceberg Yes, but you should keep correct track of what the matrices you obtain are telling you. In your case, you need to invert the role and transpose every single thing.
1d
answered Finding an order of a coset in $A/B$ where $A$ is a free abelian group and $B$ is a subgroup.
1d
revised Are the $2\times 2$ symmetric matrices a ring?
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