# All Questions

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### IMPA (Brazil) vs Iowa State University (USA) [on hold]

I was recently offered admission to Iowa State for a math PhD. I thought they were to deny me admission since they had not answer me until now (I spected an answer in March). Since I had not had a ...
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### associated prime of a module under a ring homomorphism

Let $f: A\rightarrow B$ be a homomorphism of Noetherian rings, and $M$ a $B$-module(not necessarily finitely generated). Question: Is $^af(Ass_B(M))=Ass_A(M)$? If $q$ is an associated prime of the ...
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### Prove the isomorphism of categories $Fun(\mathcal{A}\times\mathcal{B},\mathcal{C})\cong Fun(\mathcal{A},Fun(\mathcal{B},\mathcal{C})),$ [migrated]

I'm a computational engineer starting with a course of Introduction to Category Theory, and perhaps is extremely basic what I'm asking but I'm trying to learn how to make proofs in category theory ...
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### Acyclic complexes for extraordinary cohomology theories

Let $X$ be a CW complex such that for all extraordinary homology theories, if you plug $X$ into them you get the same value as plugging in a point. Must $X$ be contractible?
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### What exactly is wrong with this statement (Lucas-Penrose fallacy)? [on hold]

Statement "For every computer system, there is a sentence which is undecidable for the computer, but the human sees that it is true, therefore proving the sentence via some non-algorithmic method." ...
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### $A \wedge A \wedge A$ in Chern-Simons

I am confused with the wedging operations of Lie algebra valued differential forms. Especially, for instance, I have some problems with the Chern-Simons 3-form A \wedge dA + \frac{2}{3}A \wedge A ...
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### Graph classes which are not perfect but the stability number = clique cover numer?

I have a result for graphs whose stability number=clique cover number, which naturally includes the perfect graphs, but I'm curious about if there are other known and well-definable graph classes ...
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### automorphism group of partially ordered by divisibillity [on hold]

We define bijection $F: \aleph \to \aleph$ as follows: \begin{array}{l} {a|b\Leftrightarrow F(a)|F(b)} \\ {1\to 1} \end{array} What group is Automorphism group linked to $F$?
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### is the minimum envelope of two inrersecting convex functions convex? [on hold]

when two convex cost functions intersects, can we say that their minimum envelope is convex, which doesn't looks like convex? Again if it is not convex, then is any relaxation theorem available such ...
Is there a torsion-free group containing two elements $x$ and $y$ and a finite non-empty subset $B$ such that $B=xB \triangle yB$, where $\triangle$ denotes the symmetric difference of two sets and ...
### Example of a $G$-sphere that is not a $G$-representation sphere
Let $G$ be a finite group with the discrete topology. To set terminology: a $G$-sphere is a sphere equipped with a continuous $G$-action a $G$-representation sphere is a $G$-sphere obtained from an ...