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Results tagged with noncommutative-algebra
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user 4008
Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras
23
votes
Why does the Grothendieck group $K_0(R)$ of a ring not depend on our choice of using left mo...
Here is an alternative to Andreas proof (which if you unfold it is not so different): We have a functor $M\mapsto \mathrm{Hom}_R(M,R)=:M^\ast$ which gives both a contravariant functor from left $R$-mo …
- 22.6k
6
votes
Homological dimension of a graded ring which is like polynomial ring
I do not know the answer to your first question. As for the next two the answer
is positive; one need only slightly modify standard proofs for the usual
polynomial ring:
If $R$ is a graded ring then …
- 22.6k
3
votes
Accepted
Morphisms of a simple sheaf over an algebra to its double dual
Any $R$-homomorphism (in fact any $\mathcal O_S$-homomorphism) $M \to M^{**}$ extends to a morphism $M^{**}\to M^{**}$ (as $M$ is locally free in codimension $1$ and $M^{**}$ is the maximal extension …
- 22.6k
3
votes
Accepted
The Jacobson radical of an infinite dimensional algebra
As there seem to be some differing opinions in the comments as to whether all
irreducible representations are finite-dimensional let me give the argument I
had in mind. A module over the path algebra …
- 22.6k