All Questions
12 questions
3
votes
0
answers
391
views
Are prime ideals of finite height in the powers series ring in infinitely variables finitely generated?
Let $A:= {\mathbb F}_p[[X_1,...,X_∞]]$ be the infinitely many variables formal power series ring over ${\mathbb F}_p$, which is UFD.
Consider an arbitrary prime ideal $P$ of $A$ such that the height ...
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2
votes
1
answer
329
views
Heights of contracted ideals
Let $R$ be a non-noetherian domain. $S$ be a multiplicatively closed subset of $R$. Let $S^{-1}R$ be a localisation of $R$, where all element of $S$ is invertible. Suppose we have an ideal $I$ of $R$. ...
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2
votes
0
answers
100
views
On a certain radical of the formal power series ring $K[[X_1,X_2,\ldots,X_{\infty}]]$
Let $K$ be a field of characteristic $p > 2$ and $A_{\infty} \colon= K[[X_1,X_2,\ldots,X_{\infty}]]$ be an infinitely-many-variable formal power series ring over $K$ (the symbol $X_{\infty}$ is to ...
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1
vote
1
answer
224
views
Power series ring $\Theta[[X_1,\ldots,X_d]]$ and prime ideals
Let $\Theta$ be a domain. We shall choose $d$ elements $\theta_1,\ldots,\theta_d \in \Theta$ such that any chosen $j$ elements $\theta_{i_1},\ldots,\theta_{i_j}$ form a prime ideal $(\theta_{i_1},\...
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1
vote
2
answers
471
views
Prime ideal of $A[X_1,...,X_d]$
Let $A$ be a UFD domain, i.e. integral and for any height one prime
${\frak p}$ of $A$, we have ${\frak p} = (u_{\frak p})$ for some $u_{\frak p} \in A$.
Once and for all, we fix the algebraic ...
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1
vote
0
answers
551
views
An infinitely-many-variable formal power series ring ${\Bbb F}_p[[X_1,\ldots]]$
We shall define a infinitely-many-variable formal power series ring ${\Bbb F}_p[[X_1,\ldots]]$ as follows$\colon$
${\Bbb F}_p[[X_1,\ldots]]\colon= \underset{n \geq 1}{\varprojlim}\, {\Bbb F}_p[[X_1,\...
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1
vote
0
answers
166
views
Popescu-Neron Desingularization for K[[T_1,...,T_∞]]
Let $K[[T_1,...,T_n]]$ be a finitely many variables formal power series ring over a field $K$.
Dorin Popescu proved that there are smooth algebras $A_{\lambda}$'s which are of finite type over $K$ ...
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1
vote
0
answers
485
views
On the coherence of formal power series ring
Let $A = {\Bbb F}_p[[X_1,X_2,...]]$
be the ring of formal power series with infinitely many variables over the finite field ${\Bbb F}_p.$
$A$ consists of such formal sum elements as $\sum c_{e_1,.....
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1
vote
0
answers
201
views
Number of minimal primes for UFD
Let $R$ be a UFD which is NOT noetherian. It is well-known that $R$
is a Krull ring. Let $I$ be an ideal of $R$ such that the height of $I$
is $d$ which is finite.
Question. Is the number of minimal ...
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0
votes
2
answers
2k
views
Tensor products of two domains
Let $R$ be an integral noetherian regular local ring. Let $S$ be a noetherian integral domain such that $S/R$ is finite.
That is, $R \subset S$ and the surjection $R^{\oplus n} \twoheadrightarrow S$ ...
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0
votes
1
answer
343
views
Relative Bertini Theorem
Let
$A \colon= {\Bbb C}[S_1,\ldots,S_n]$ with $1 \leq n < \infty$
$B \colon= A[X_1,\ldots,X_d]$ with $2 \leq d < \infty$.
$O \colon= (0,\ldots,0)$ be the origin of ${\mathrm{Spec}}\,B$.
...
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0
votes
0
answers
154
views
Determinant of a special matrix in characteristic $p$
Let $K$ be a field of characteristic $p > 0$. Choose $p^i$ numbers of elements $c_1,\ldots,c_{p^i} \in K$ and consider the determinant $D$ of the following matrix$\colon$
\begin{pmatrix}\label{...
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