2 citations · 5 across the 8 of their papers we have counts for
11 papers
Group equations with abelian predicates
Laura Ciobanu, Albert Garreta
In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work…
The Diophantine problem in finitely generated commutative rings
Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov
We study systems of polynomial equations in infinite finitely generated commutative associative rings with an identity element. For each such ring we obtain an interpretation b…
Metabelian groups: full-rank presentations, randomness and Diophantine problems
Albert Garreta, Leire Legarreta, Alexei Miasnikov +1
We study metabelian groups given by full rank finite presentations in the variety of metabelian groups. We prove that …
Simple groups with infinite verbal width and the same positive theory as free groups
Montserrat Casals-Ruiz, Albert Garreta, Ilya Kazachkov +1
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these…
On the positive theory of groups acting on trees
Montserrat Casals-Ruiz, Albert Garreta, Javier de la Nuez González
We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coinc…
On equations and first-order theory of one-relator monoids
Albert Garreta, Robert D. Gray
We investigate systems of equations and the first-order theory of one-relator monoids. We describe a family of one-relator monoids of the form $\langle A\mid w=1\rang…