5 problems

Gelfand-transform criterion. $F\in SL_n(R)$ belongs to $E_n(R)$ if and only if

Let $dim=3$, $4$, or $5$. Let $\mathcal{A}$ be either an imaginary quadratic field when $dim=3$, a rational definite quaternion algebra equipped with an orthogonal involution…

Hardy-algebra elementary-generation conjecture.

Let $\mathbb Z[t,t^{-1}]$ be the Laurent polynomial ring in one variable over the integers, let $SL_2(\mathbb Z[t,t^{-1}])$ be its special linear group, and let…

Let $A$ be a ring endowed with an increasing ${\mathbb N}$-filtration $F$, and suppose that the associated graded ring of $A$ is a domain. For each integer $n\geq 2$, let $F(0)$ de…