Simone Virili
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Registered User
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I'm a PhD student at the Universitat Autònoma de Barcelona.
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1d |
asked | Amenable group rings embeddable in skew fields |
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Mar 22 |
asked | Minimal prime ideals of a group ring |
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Feb 24 |
comment |
Existence of nice Folner sequences @Mark: Thanks for your answer and comment! I'm trying to understand how some dynamical results in dynamical systems of the form $G\times M\to M$ (with $G$ amenable and $M$ an Abelian discrete group) generalize from the case when $G$ is Abelian (e.g. $\mathbb Z^n$) to the general situation. I admit that my intuition is still not that good in the non-commutative case! |
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Feb 24 |
accepted | Dual concept for the p-primary component |
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Feb 24 |
comment |
Existence of nice Folner sequences @Misha: well... in that case ${B_n:n\in\mathbb N}$ is a Folner sequence so the interesting case is when you have exponential growth... |
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Feb 23 |
asked | Existence of nice Folner sequences |
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Feb 23 |
revised |
Dual concept for the p-primary component added 346 characters in body; added 194 characters in body; added 1 characters in body |
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Feb 23 |
answered | Dual concept for the p-primary component |
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Feb 14 |
comment |
Partial order relation on subsets Essentially you are taking strictly increasing maps from {1,...,k} to {1,...,n}. Than, given two strictly increasing maps $f,g:\{1,...,k\}\to \{1,\dots,n\}$ you say that $f\prec g$ if $f(i)\leq g(i)$ for all $i\in\{1,\dots,k\}$. I would call it just a pointwise order... I cannot help you with any reference. |
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Jan 28 |
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What is the dual of a pre-injective map? no problem, it is nice to have this motivation for my question here |
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Jan 28 |
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What is the dual of a pre-injective map? Yes I did know such connection, which is in fact part of the motivation for my question... |
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Jan 28 |
asked | What is the dual of a pre-injective map? |
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Dec 19 |
comment |
On topology of p-adic numbers. actually this happens for any topological group admitting a base of neighborhoods given by subgroups |
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Dec 18 |
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Localization of a pure-injective module is pure-injective? what is your setting? What do mean by "localization"? This could be an interesting question, it would be nice to have some more details (do you refer to a left or right Ore localization? are you thinking to modules over a commutative ring? ...). |
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Dec 15 |
answered | Finite / uniquely divisible abelian groups |
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Dec 15 |
comment |
torsion theories localizing the base ring to the same ring yes, I was not saying that the localization is equivalent to $-\otimes_RR_1$, I was just saying that maybe, when these two functors are different, maybe they have the same kernel... do you have some easy counterexample? |
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Dec 15 |
revised |
torsion theories localizing the base ring to the same ring deleted 8 characters in body |
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Dec 15 |
answered | torsion theories localizing the base ring to the same ring |
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Dec 12 |
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How should one look at the set of compatible ring structures on a given group? Even if the point of view is completely different, in the second volume (if I remember correctly) of "Infinite Abelian Groups" by Laszlo Fuchs, there is a nice discussion about the possible ring structures on a given Abelian group $G$. (probably you are aware of this, but it is not always possible to find such a ring structure on a given group) |
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Dec 4 |
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Does Mittag-Lefflerness descend? It does not answer completely your question but I suggest you to have a look to this paper arxiv.org/pdf/0704.3690v1.pdf In particular Example 1.6 and Proposition 1.7 discuss similar matters |
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Dec 3 |
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Are amenable groups topologizable? probably Corollary 3 on page 213 in mscand.dk/article.php?id=2006 will help... |
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Dec 2 |
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Noncommutative Localization “from scratch” @Martin: the commutative setting is really different!!! The common point of view for localizing a module $M$ on a commutative ring $R$ with respect to a multiplicative subset $\Sigma\subseteq R$ is to view the elements of $\Sigma$ as endomorphisms of $M$ and so take the direct limit of $|\Sigma|$-many copies of $M$ with these transition maps. When $R$ is not commutative you cannot do so if $\Sigma$ is not included in the center $Z(\Sigma)$. This is a non-trivial complication (in concrete situations it makes really a lot of difference, I can give you concrete examples)! |
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Dec 2 |
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Are amenable groups topologizable? unfortunately it seems that the bohr topology is T2 only for MAP groups... is there any known example of amenable non-MAP group (with the discrete topology)? |
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Dec 1 |
accepted | ring with a condition |
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Nov 27 |
revised |
ring with a condition added 192 characters in body |
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Nov 27 |
revised |
ring with a condition deleted 1 characters in body |
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Nov 27 |
revised |
ring with a condition added 312 characters in body; added 16 characters in body |
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Nov 27 |
revised |
ring with a condition added 189 characters in body |
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Nov 27 |
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ring with a condition well... hard to believe... even if you changed your question, still your condition cannot be verified when $x\in I$. I strongly suggest you explain us context and motivation! |
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Nov 27 |
answered | ring with a condition |
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Nov 27 |
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ring with a condition another observation. How is it possible to satisfy your second condition for all $x,y\in R$? In particular, if $x\in I$, then, as $I$ is a right ideal, $xry$ belongs to $I$ for all $r$ and all $y$. So... for $x\in I$, the set {$r\in R|xry\notin I$} is always empty. For example, take $x=0$ or $y=0$, you will see that your second condition is impossible to satisfy. So the answer is "NO!" there is no such ring:) |
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Nov 27 |
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Cocomplete but not complete abelian category Well... I accepted the answer becuase the bounty was finishing and I preferred to give the full points to someone that at least attempted a solution. This bounty rule is probably not the best but without the bounty I don't think so many people would have been interested in this question. I want to thank you all for the nice constructions, that will be useful to me anyway! I hope someone will be able to produce a counter-example sooner or later:) |
