16
votes
3answers
1k views
Which rings are subrings of matrix rings?
In this question, all rings are commutative with a 1, unless we explicitly say
so, and all morphisms of rings send 1 to 1.
Let A be a Noetherian local integral domain. Let T be a …
3
votes
1answer
262 views
Is there an example of Gibbs measure that is not a weak limit of finite volume Gibbs measure ?
Consider the first neighbors Ising model in $\mathbb Z^2$, with the Hamiltonian in the finite volume $\Lambda\subset\mathbb{Z}^2$ given by
$$
H_{\Lambda}(\sigma|\omega)=-J\sum_{i, …
5
votes
2answers
192 views
What condition on a “bibundle between categories” generalizes “right-principal bibundle between groupoids”?
My question is long on background and motivation, and almost but not quite answered over at the nLab. I'll write up a bunch before asking my question (feel free to skip to the end …
9
votes
1answer
1k views
Sequence that converge if they have an accumulation point
I am looking for classes of sequence, that converge iff they contain a converging sub-sequence.
The basic example of such sequences are monotone sequences of real numbers.
A more …
1
vote
0answers
150 views
Marginals and Convex Sets
I am looking for a weak convergence of marginals result, in the following type of situation. References to 'related' situations are also very much appreciated.
I have a collection …
2
votes
1answer
124 views
systems of parameters vs. minimal “exhausting” systems in a Noetherian local ring
Hello,
Probably this is a very easy question.
Fix a Noetherian local ring $A$, and an $A$-module of finite type $M$.
Lets call a system $ x_1 , \ldots , x_m \in \mathfrak{m}$ $M$ …
7
votes
4answers
980 views
[solved] sequent calculus as programming language
intuitionistic logic ~ programming
natural deduction ~ lambda-calculus
Hilbert system ~ combinatory logic {S, K}
Gentzen system=sequent calculus ~ ?
What would you write in pla …
1
vote
1answer
930 views
Confusing definitions in Liu’s Algebraic geometry and arithmetic curves?
In Qing Liu's book Algebraic geometry and arithmetic curves I came across several confusing definitions. Several times he defines a notion only for a subclass of schemes/morphisms …
11
votes
1answer
386 views
The space of compact subspaces of $R^\infty$ homotopy equivalent to a given finite complex.
Let $X$ be a finite (CW or simplicial - doesn't matter) complex and consider the space of all compact subspaces of $R^\infty$ which are homotopy equivalent to $X$, topologized say …
4
votes
2answers
545 views
Set Theory and Definability
Let $\mathcal{G} = (G,\in)$ be some $\mathfrak{L}$ = {$\in$} structure (for this question a model of ZFC). Let $M$ be some definable class (using Jech's term) and $E$ some class-re …
3
votes
2answers
473 views
Different forms of compactness and their relation
Given a topological space X one can define several notion of compactness:
X is compact if every open cover has a finite subcover.
X is sequentially compact if every sequence has …
0
votes
0answers
142 views
Generalized Fibonacci sequences [closed]
Why Fibonacci sequence start at 0, Tribonacci sequence with 0,0, Tetranacci with 0,0,0, etc. Can this sequences starts at 1. Has any good reasons for that. These sequences arise in …
1
vote
3answers
895 views
Derived functor
Let $F:A\longrightarrow B$ be a left exact functor of Abelian categories. My question is about the derived functor $RF: D(A)\longrightarrow D(B)$.
Let $X$ be an object of $A$. If …
8
votes
2answers
889 views
What are picard categories, where can I learn more about them, and why should I care to?
I have the category-theoretic background of the occasional stroll through Mac Lane's text, so excuse my ignorance in this regard. I was trying to learn all that I could on the subj …
0
votes
2answers
723 views
post correspondence problem
I have read a couple of proofs for the undecidability of the post correspondence problem, but neither reference gave a concrete example of two lists of words over a fixed alphabet …
