6 papers
Bisoluble and Binilpotent Skew Braces of Finite Morley Rank
Maria Ferrara, Moreno Invitti, Marco Trombetti +1
A connected skew brace of finite Morley rank is left nilpotent (resp. weakly soluble) whenever the additive and multiplicative groups are nilpotent (resp. are soluble and the left…
Almost cohomology of finite-dimensional Lie rings
Moreno Invitti
We introduce almost cohomology groups for Lie rings definable in finite-dimensional theory. In particular, we define the 0th and 1st almost cohomology groups of a Lie ring module.…
Omega-categorical groups and rings of finite dimension
Moreno Invitti
We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.
Endogenies and linearization in the non-virtually connected case
Moreno Invitti
We prove a linearization theorem for pre-rings of endogenies acting on a definable abelian group of finite dimension. Observe that no assumptions on the connectivity of A are made.…
Lie rings in finite-dimensional theories
Moreno Invitti
We study Lie rings definable in a finite-dimensional theory, extending the results for the finite Morley rank case. In particular, we prove a classification of Lie rings of dimensi…
Skew Braces from a model-theoretic point of view 1
Maria Ferrara, Marco Trombetti, Moreno Invitti +1
Skew braces are one of the main algebraic tools controlling the structure of a non-degenerate bijective set-theoretic solution of the Yang-Baxter equation. The aim of this paper is…