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Results tagged with ra.rings-and-algebras
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user 24447
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
9
votes
Towards the complex unit conjecture
There are no such obstacles a posteriori since the complex unit conjecture is false.
- 3,736
2
votes
Group ring and left zero divisor
If $G$ is torsion-free then the question of reversibility of $K[G]$ (that is, does $ab = 0$ imply $ba = 0$) is in fact equivalent to the zero divisor conjecture, for any field $K$.
Connell showed that …
- 3,736
1
vote
Zero divisor conjecture for finite fields
For a fixed group $G$, the zero divisor conjecture over $\mathbb{C}$ is implied by the zero divisor conjecture over an algebraically closed field of positive characteristic, so in particular it would …
- 3,736
6
votes
Accepted
Examples of Noetherian integral group ring
There are no known examples of groups with Noetherian integral group rings other than virtually polycyclic groups. The following result and subsequent text is quoted from
Kropholler, Peter; Lorensen, …
- 3,736
8
votes
What is the current status of the Kaplansky zero-divisor conjecture for group rings?
Since there's been a request for an update on the zero divisor conjecture, let me give one. The zero divisor conjecture is open. I'll update this answer if I hear otherwise.
Alain already mentioned th …
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50
votes
What is the current status of the Kaplansky zero-divisor conjecture for group rings?
Apologies for the self-promotion, but there is now a counterexample to the unit conjecture (U) with $K=\mathbb{F}_2$ and virtually abelian $G = \langle a, b \,|\, (a^2)^b=a^{-2}, (b^2)^a=b^{-2} \rangl …
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