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4
votes
Constant term extraction using combinatorial Nullstellensatz
The argument below works only for odd $r$. This is annoying, but I do not see how to modify it for even $r$. Of course, there is a simple argument without CN, but I guess it is not what you ask for.
W …
7
votes
Idempotent Laurent polynomials (in noncommuting variables)
No, it can not. $R$ is a group ring of the free group with $n$ generators. This group is locally indicable (any non-trivial subgroup has a homomorphism onto $\mathbb{Z}$), thus by result of Higman (Hi …