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Results tagged with ra.rings-and-algebras
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user 21724
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
6
votes
1
answer
702
views
Characteristic polynomial of a generic n*n matric
Let $K$ be a field, and $F_K$ be the fraction field of the polynomial ring $R_K$ in $n^2$ indeterminates $X_{11},X_{12},...,X_{nn}$ over $K$.
Now set $A = (X_{ij})_{i,j} \in M_n (F_K)$, and let $\chi_ …
- 7,249
2
votes
0
answers
95
views
Is the positive part of an algebraic bilateral p-adic convergent power series algebraic?
Let $\mathbb{Z}_p \{ X\}$ and $\mathbb{Z}_p \{ X , X^{-1}\}$ be the henselizations of $\mathbb{Z}_p [X]$ and $\mathbb{Z}_p [ X , X^{-1}]$ with respect to the ideals $p\mathbb{Z}_p [X]$ and $p\mathbb{Z …
- 7,249
4
votes
1
answer
422
views
Ring structrures on R^n
Consider a commutative ring $A= ( \mathbb{R}^n , + , \times) $, where $+$ is the usual one. Assume further that $ \times $ is continuous (with respect to the usual topology). Let $H$ be the set of non …
- 7,249
5
votes
0
answers
250
views
A question on symmetric functions
Let $0 \leq m \leq n$ be integers. The group $S_n$ of permutations acts on the ring $\mathbb{Z}[X_1,\dots,X_n]$ by permuting the coordinates, with fixed subring $\mathbb{Z}[\sigma_1,\dots,\sigma_n]$, …
- 7,249
5
votes
Accepted
Coherent subsheaf of co-admissible modules of Schneider and Teitelbaum
The map $A_{q_n} \otimes_{A_{q_{n+1}}} N_{n+1} \rightarrow N_n$ is surjective, by definition of $N_n$. To show that it is injective, it suffices to show that the composition $A_{q_n} \otimes_{A_{q_{n+ …
- 7,249
1
vote
Accepted
What are the fixed points of $\alpha^n-\mu_j$ for a fixed $j$?
Let $L$ be the line generated by $\underline{\mu} = (\mu_1,\dots,\mu_s)$ in $V = \mathbb{C}^s$, and consider a projection $p : V \rightarrow V$ onto $L$, with kernel $H$. Any polynomial function of th …
- 7,249