All Questions
Tagged with p-adic-numbers ra.rings-and-algebras
7 questions
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Can every $\ast$-algebra be represented in this space of matrices?
Let $k$ be a field with characteristic $0$. For every set $X$, let $\mathcal{B}(X)$ be the set of (possibly infinite) matrices $T = (T_{x,y})_{x,y \in X}$ with coefficients in $k$ such that in each ...
- 1,485
3
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1
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564
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Is there a classification of the $p$-adic normed division algebras?
A normed division algebra over $\mathbb{R}$ is a pair $(A,\lVert{-}\rVert)$ with
$A$ an $\mathbb{R}$-algebra with a unit $1_A$;
$\lVert{-}\rVert\colon A\to\mathbb{R}_{\geq0}$ a norm on $A$;
such ...
- 11.8k
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269
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If two monic polynomials of $\mathbb{Z}_p[X]$ (p-adic integer coefficient) are relatively prime modulo p, then do they generate $\mathbb{Z}_p[X]$?
I'm currently reading a paper of Rene Schoof, and I got stuck in a line. And I'm trying to check the above sentence.
Although that seems to be elementary, I hope someone can give me a counterexample ...
- 1,013
6
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698
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Jacobson radical of a tensor product
Let $R$ be a commutative ring and $A_1$, $A_2$ be $R$-algebras. Is there any general mean to compute the Jacobson radical of the tensor product $A_1\otimes_R A_2$ in terms of ${\rm Rad}(A_i )$, $i=1,2$...
- 6,349
6
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224
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Specifying cokernels of all powers of $p$-adic matrix
Given a matrix $A \in M_d(\mathbb{Z}_p)$ (with nonzero determinant), viewed as a map $\mathbb{Z}_p^d \to \mathbb{Z}_p^d$, I am interested in the sequence of abelian $p$-groups $\{coker(A^n)\}_{n \geq ...
- 568
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197
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Name of some commutative ring akin to $p$-adics
I need help in identifying the naming convention of some commutative ring described below.
Let $p$ be a prime, let $k$ be a positive integer, and let $$\textbf{e} = (e_0,\ldots,e_{k-1})$$ be a list ...
- 103
5
votes
1
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365
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Why is this a lattice?
Why is $\text{SL}_3(\mathbf{Z}[1/2])$ a lattice in $\text{SL}_3(\mathbf{R})\times\text{SL}_3(\mathbf{Q}_2)$? Discreteness is pretty clear, but why finite covolume? I understand why $\text{SL}_3(\...
- 9,720