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4
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1answer
193 views

Separable and Fin. Gen. Projective but not Frobenius?

Let R be a commutative ring, and A an R-algebra (possibly non-commutative). Then A is separable if it is (fin. gen.) projective as an (A tensor_R A^op)-algebra. Suppose further that A is fin. gen. ...
17
votes
1answer
1k views

When should I expect a quiver with potential to be rigid?

This question is pretty technical, but there are some very smart people here. Fix a quiver Q, WITH oriented cycles. Let k[[Q]] be the completed path algebra. (Like the path algebra, but we allow ...
5
votes
7answers
1k views

Hochschild/Cyclic Homology of von Neumann Algebras: Useless?

Hochschild homology gives invariants of (unital) $k$-algebras for $k$ a unital, commutative ring. If we let our algebra $A$ be the group ring $k[G]$ for $G$ a finite group, we get group homology. ...
5
votes
2answers
882 views

What is an example of a ring in which the intersection of all maximal two-sided ideals is not equal to the Jacobson radical?

What is an example of a ring in which the intersection of all maximal two-sided ideals is not equal to the Jacobson radical? Wikipedia suggests that any simple ring with a nontrivial right ideal would ...
10
votes
2answers
468 views

Ideals in Factors

One can easily prove that factors have no nontrivial ultraweakly closed 2-sided ideals as these are equivalent to nontrivial central projections. One can also show type $I_n$, type $II_1$, and type ...
16
votes
5answers
3k views

Can a quotient ring R/J ever be flat over R?

If R is a ring and J⊂R is an ideal, can R/J ever be a flat R-module? For algebraic geometers, the question is "can a closed immersion ever be flat?" The answer is yes: take J=0. For a less ...
7
votes
1answer
525 views

Is there a good computer package for working with complexes over non-commutative rings?

I'm interested in doing computations with certain non-commutative rings, most of which involve taking derived tensor products. Does anyone know of a computer algebra package which will find ...