Timeline for zero divisors of group ring when the group is abelian

6 events

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Oct 18, 2021 at 0:28	comment	added	HuiRong		@BenjaminSteinberg Yes, I also consider groups $G$ which are not finitely generated, such as quotient groups of $\mathbb{C}$ (complex numbers).
Oct 16, 2021 at 18:31	comment	added	Benjamin Steinberg		@JosephVanName, what if the group is not finitely generated?
Oct 16, 2021 at 15:45	comment	added	Joseph Van Name		And the ideal $\langle x_{1}^{a_{1}}-1,\dots,x_{r}^{a_{r}}-1\rangle$ in $\mathbb{C}[x_{1},\dots,x_{r+s}]$ is precisely the set of all polynomials $p$ such that $p(u_{1},\dots,u_{r},x_{r+1},\dots,x_{r+s})=0$ whenever $u_{1}^{a_{1}}=\dots=u_{r}^{a_{r}}=1$.
Oct 16, 2021 at 14:17	comment	added	Joseph Van Name		Have you tried writing $\mathbb{C}[G]$ as $\mathbb{C}[x_{1},\dots,x_{r+s}]/\langle x_{1}^{a_{1}}-1,\dots,x_{r}^{a_{r}}-1\rangle$ when $G$ is finitely generated?
Oct 16, 2021 at 12:45	history	edited	YCor		edited tags; edited tags
Oct 16, 2021 at 12:42	history	asked	HuiRong	CC BY-SA 4.0