All Questions
Tagged with derivations commutative-algebra
4 questions
5
votes
1
answer
107
views
Existence of $\mathbb{N}$-grading compatible with LNDs.
Let $B$ be a finitely generated integral $\mathbb{C}$-domain. Let $\partial:B\to B$ be a LND, locally nilpotent derivation, i.e. a $\mathbb{C}$-linear map satisfying
Leibniz rule: $\partial(fg)=f\...
- 1,479
1
vote
0
answers
77
views
Understanding proof of the Eisenbud, Commutative Algebra, Theorem 16.24 ($\Omega_{S/R} \cong I/I^2 $ , where $I = \ker (\mu : S \otimes_R S \to S)$).
I am reading the Eisenbud, commutative algebra, proof of Theorem 16.24 and some question arises.
First, let me note some associated definition and theorem.
Definiton. If $S$ is a ring and $M$ is an $S$...
- 3,072
1
vote
0
answers
112
views
On the free resolution of module of Kahler differentials of a hypersurface
Let $k$ be an algebraically closed field of characteristic $0$. Consider the local ring $S=k[x_1,...,x_d]_{(x_1,...,x_d)}$, and call its maximal ideal $\mathfrak m$. Let $f\in k[x_1,...,x_d]$ be such ...
- 557
0
votes
0
answers
31
views
Relation between algebraic and analytic derivations in $\mathcal C(\mathbb R)$
Let $A,B$ be two $\mathbb R$-algebras. By an $\mathbb R$-linear (algebraic) derivation from $A$ to $B$, we mean a group homomorphism $D:A\rightarrow B$ which contains $\mathbb R$ in its kernel and ...
