3 papers
math.GR2026
The Diophantine Problem in Wreath Products of Groups
Michael Catli, Alexei Myasnikov
We study the Diophantine problem in restricted wreath products of groups. Write , where is the passive factor and is the active factor. The main results demonstra…
math.LO2024
Nonstandard polynomials: algebraic properties and elementary equivalence
Alexei Myasnikov, Andrey Nikolaev
We solve the first-order classification problem for rings of polynomials and Laurent polynomials with coefficients i…
math.NT2023
The Diophantine problem in Chevalley groups
Elena Bunina, Alexey Miasnikov, Eugene Plotkin
In this paper we study the Diophantine problem in Chevalley groups , where is an indecomposable root system of rank , is an arbitrary commutative ring with $…