Talk:Kaplansky's conjectures

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There are numerous conjectures of Irving Kaplansky, for example a list on Hopf algebras also. So a better title could be sought for the page.

Zero-divisor conjecture is probably better, but there is also another such named conjecture, in commutative algebra.

Charles Matthews 08:45, 16 February 2006 (UTC)

A counterexample to the unit conjecture?

From an edit i undid (this is too early to be added to the article but if accepted by the math community should be put back so I saved it here for future reference) :

"In a pre-print from 2021, Gardam produced an example of a group $G$ over $\mathbb {F} _{2}$ such that $\mathbb {F} _{2}[G]$ contains a non-trivial unit. If correct, this would hence show that the Kaplansky unit conjecture is false."

jraimbau (talk) 12:21, 24 February 2021 (UTC)

As far as I can tell the preprint looks good (did not check it yet) so hopefully it'll be accepted in a journal soon and we can add it to the article. jraimbau (talk) 12:25, 24 February 2021 (UTC)

Gardam's preprint mentions that the unit conjecture appears in Graham Higman's DPhil Thesis 'The units of group-rings'. I think this should be mentioned but without access to the thesis myself, and the only evidence being a preprint maybe we should hold off unless someone can check what it says in the thesis or find a refereed source for the observation?Billlion (talk) 08:11, 16 April 2021 (UTC)

References