Ruiwen Dong

collaborators

5 papers

cs.LO2026

The Skolem Problem in rings of positive characteristic

Ruiwen Dong, Doron Shafrir

We show that the Skolem Problem is decidable in finitely generated commutative rings of positive characteristic. More precisely, we show that there exists an algorithm which, given…

math.GR2025

The Identity Problem in the special affine group of $Z^{2}$

Ruiwen Dong

We consider semigroup algorithmic problems in the Special Affine group $SA (2, Z) = Z^{2} ⋊ SL (2, Z)$ , which is the group of affine…

math.NT2025

S-unit equations in modules and linear-exponential Diophantine equations

Ruiwen Dong, Doron Shafrir

Let $T$ be a positive integer, and $M$ be a finitely presented module over the Laurent polynomial ring $Z_{/ T} [X_{1}^{\pm}, \dots, X_{N}^{\pm}]$ . We consider S-unit…

math.GR2025

Submonoid Membership in n-dimensional lamplighter groups and S-unit equations

Ruiwen Dong

We show that Submonoid Membership is decidable in n-dimensional lamplighter groups $(Z / p Z) ≀ Z^{n}$ for any prime $p$ and integer $n$ . More generally, we…

math.GR2025

The Identity Problem in virtually solvable matrix groups over algebraic numbers

Corentin Bodart, Ruiwen Dong

The Tits alternative states that a finitely generated matrix group either contains a nonabelian free subgroup $F_{2}$ , or it is virtually solvable. This paper considers two decision…

The Skolem Problem in rings of positive characteristic

The Identity Problem in the special affine group of Z2

S-unit equations in modules and linear-exponential Diophantine equations

Submonoid Membership in n-dimensional lamplighter groups and S-unit equations

The Identity Problem in virtually solvable matrix groups over algebraic numbers

The Identity Problem in the special affine group of $Z^{2}$