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Results tagged with noncommutative-algebra
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user 750
Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras
6
votes
1
answer
334
views
A potential resolution of $R/r$
The DGA
For $k$ some field, let $R$ be a $k$-algebra, and let $r\in R$.
Define a differential graded algebra $\mathbf{R}_r$ as follows. As a graded algebra, it is isomorphic to $R\langle t\rangle$, t …
- 13k
3
votes
0
answers
163
views
Pulling out factors in a Noetherian Domain
Let $R$ be a Noetherian domain (not-necessarily commutative), and let $S$ be a Noetherian subring of $R$. An element $r\in R$ is left $S$-irreducible if, for any $s\in S$ and $r' \in R$ with $sr'=r$, …
- 13k
7
votes
1
answer
566
views
Depth Zero Ideals in the Homogenized Weyl Algebra
Let $\mathcal{D}$ be the $n$th Weyl algebra $ \mathcal{D} :=k[x_1,...,x_n,\partial_1,...,\partial_n] $, where $\partial_ix_i-x_i\partial_i=1$.
Let $\widetilde{\mathcal{D}}$ be its Rees algebra, whi …
- 13k
26
votes
1
answer
990
views
Idempotents in Rings of Differential Operators
Differential Operators on General Commutative Rings
Let k be an algebraically closed field of characteristic zero, and let R be a commutative k-algebra. Then a (Grothendieck) differential operator on …
- 13k