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Results tagged with noncommutative-algebra
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user 3233
Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras
2
votes
2
answers
967
views
Torsion in tensor products over noncommutative rings
I know that the problem of torsion in tensor products, even of torsion free modules, is a very delicate thing. Unfortunately i don't have a deeper insight into this subject, so i don't know how things …
- 1,391
2
votes
2
answers
394
views
Are morphisms of finite length modules determined by the behaviour of the simple modules?
Assume we have a noncommutative ring $R$ with exactly 2 non-isomorphic simple left modules $S_1$ and $S_2$ (up to isomorphism) and an $R$-bimodule $M$, which switches the simples, i.e. $M\otimes_R S_1 …
- 1,391
1
vote
1
answer
273
views
Q-Divisor and Determinant Map on a Maximal Order
Given a smooth projective surface $X$, let $A$ be a sheaf of maximal orders in a division ring.
Let us for simplicity assume $A$ ramifies in one curve $C$ with ramification index $e$. Let $A^*$ be the …
- 1,391
5
votes
1
answer
2k
views
Length of a module over different rings
Given a regular local ring $(R,m)$ and a finitely generated $R$-algebra $S$, which is free as an $R$-module. Let $M$ be a left $S$-module of finite length, $\ell_S(M)=r<\infty$.
Under what conditions …
- 1,391
1
vote
1
answer
405
views
Morphisms of a simple sheaf over an algebra to its double dual
Given a smooth and projective surface $S$ over an algebraically closed field $k$ and a sheaf of Azumaya algebras $R$, i.e. $R$ is a locally free $O_S$-module of finite rank. Let $M$ be a coherent and …
- 1,391