Doron Shafrir

activity

20242026

collaborators

6 papers

math.NT2026

Skolem-Mahler-Lech in rings of positive characteristic: a shorter proof and a multi-dimensional generalization

Ruiwen Dong, Doron Shafrir

Let $R$ be a commutative ring and $f (a_{1}, \dots, a_{n}) = \sum_{i = 1}^{k} r_{i 1}^{a_{1}} \dots r_{in}^{a_{n}} m_{i}$ be a linear-exponential map over an $R$ -module $M$ . Dong and Shafrir (20…

cs.LO2025

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.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.GR2024

Sections of Submonoids of Nilpotent Groups

Doron Shafrir

We show that every product of f.g.\ submonoids of a group $G$ is a section of a f.g.\ submonoid of $G \times H_{5} (Z)$ , where $H_{5} (Z)$ is a Heisenberg group. This g…

math.GR2024

Is decidability of the Submonoid Membership Problem closed under finite extensions?

Doron Shafrir

We show that the rational subset membership problem in $G$ can be reduced to the submonoid membership problem in $G \times H$ where $H$ is virtually Abelian. We use this to show th…

math.GR2024

Bounded Generation of Submonoids of Heisenberg Groups

Doron Shafrir

If $G$ is a nilpotent group and $[G, G]$ has Hirsch length $1$ , then every f.g. submonoid of $G$ is boundedly generated, i.e. a product of cyclic submonoids. Using a reduction of Bo…