2 citations · 3 across the 5 of their papers we have counts for
7 papers
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 …
Diophantine problems in solvable groups
Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov
We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free s…
Studying the Diophantine problem in finitely generated rings and algebras via bilinear maps
Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov
We study systems of polynomial equations in several classes of finitely generated rings and algebras. For each ring (or algebra) in one of these classes we obtain an interpreta…
Low-complexity computations for nilpotent subgroup problems
Jeremy Macdonald, Alexei Miasnikov, Denis Ovchinnikov
We solve the following algorithmic problems using TC0 circuits, or in logspace and quasilinear time, uniformly in the class of nilpotent groups with bounded nilpotency class and ra…
Random nilpotent groups, polycyclic presentations, and Diophantine problems
Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov
We introduce a model of random f.g., torsion-free, -step nilpotent groups (in short, -groups). To do so, we show that these are precisely the groups that admit a presentati…
Full rank presentations and nilpotent groups: structure, Diophantine problem, and genericity
Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov
We study finitely generated nilpotent groups given by full rank finite presentations in the variety of nilpotent groups of class at mo…