All Questions
4 questions
3
votes
0
answers
152
views
Flatness of certain $R \subseteq \mathbb{C}[x,y]$
The two-dimensional Jacobian Conjecture over $\mathbb{C}$ says the following:
Let $p,q \in \mathbb{C}[x,y]$ satisfy $\operatorname{Jac}(p,q):=p_xq_y-p_yq_x \in \mathbb{C}-\{0\}$.
Then $\mathbb{C}[p,q]=...
- 2,837
3
votes
1
answer
238
views
Flatness of certain subrings
The following question appears, more or less, here:
Let $k$ be an algebraically closed field of characteristic zero and let $S$ be a commutative $k$-algebra
(I do not mind to further assume that $S$ ...
- 2,837
2
votes
2
answers
789
views
When $mB \neq B$? $m$ is a maximal ideal of $A$, $A \subseteq B$
The following is a question I have asked here without receiving any comments, therefore I post it here:
Let $A \subseteq B$ be commutative rings, $m$ a maximal ideal of $A$.
When $mB \neq B$?
This ...
- 2,837
7
votes
1
answer
752
views
Injective flat module
Let $R$ be a (right noetherian) ring. Is there always a right $R$-module which is both flat and injective? If $R$ is an integral domain, then the answer is indeed yes, as the quotient field is such.
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- 409