All Questions
7 questions
5
votes
2
answers
754
views
A version of Hilbert's Nullstellensatz for real zeros
$\newcommand\R{\Bbb R}$Let $Q(x_1,\dots,x_n)\in\R[x_1,\dots,x_n]$ be an irreducible polynomial such that the dimension of the set $Z:=\{(x_1,\dots,x_n)\in\R^n\colon Q(x_1,\dots,x_n)=0\}$ (defined, say,...
- 3,599
3
votes
0
answers
74
views
Locally compact rings with reciprocals
A topological field is defined to be a topological ring $F$ with reciprocals such that the reciprocal function $F\setminus\{0\} \to F\setminus\{0\}$ is continuous. Locally compact topological fields ...
- 974
5
votes
1
answer
339
views
Can completely multiplicative functions be extended to $\overline{\mathbb{Q}}$ or further?
I'm looking for a subject of study that handles the following question. I'm not the most familiar with algebra; I have a strong working knowledge and that's about it, but I've been considering ...
- 348
3
votes
0
answers
96
views
Luroth's theorem for Discrete valuation rings?
Luroth's theorem states that if $k$ is a field and $L$ is a field extension of $k$ such that $k \subset L \subseteq k(X)$, then $L=k(f(X))$ for some $f(X) \in k(X) $ . My question is ; is there any ...
CommunityBot
- 1
3
votes
0
answers
112
views
Indecomposablity in purely inseparable extensions
Let $k$ be a field of characteristic $p$ (e.g. the separable closure of $\mathbb{F}_p(t)$) and consider the extension $k(x)/k$ where $x^p\in k$ but $x$ does not. Consider a (finitely generated) ...
- 63.9k
4
votes
1
answer
396
views
A generalization of the discriminant of a polynomial
Let $\mathbb{K}$ be a field and let $f \in \mathbb{K}[x]$ be a monic polynomial of degree $n$. Suppose that $\alpha_1, \ldots, \alpha_n$ are all the roots of $f$ (in some algebraic closure of $\mathbb{...
- 22.5k
2
votes
1
answer
569
views
Field extension and nilpotent element
Let $k$ be an algebraically closed field of characteristic $p>0$, $A$ a regular local noetherian $k$-algebra, $B$ another local noetherian $k$-algebra, $f:A \to B$ an injective ring homomorphism of ...
- 28.7k