10 citations · 30 across the 14 of their papers we have counts for
8 papers · 1 filter
Decidability of the theory of modules over Prüfer domains with dense value groups
Lorna Gregory, Sonia L'Innocente, Carlo Toffalori
We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideal…
The torsionfree part of the Ziegler spectrum of orders over Dedekind domains
Lorna Gregory, Sonia L'Innocente, Carlo Toffalori
We study the R-torsionfree part of the Ziegler spectrum of an order Λover a Dedekind domain R. We underline and comment on the role of lattices over Λ. We describe the torsionfree…
A factorisation theory for generalised power series and omnific integers
Sonia L'Innocente, Vincenzo Mantova
We prove that in every ring of generalised power series with non-positive real exponents and coefficients in a field of characteristic zero, every series admits a factorisation int…
Decidability of the theory of modules over Prüfer domains with infinite residue fields
Lorna Gregory, Sonia L'Innocente, Gena Puninski +1
We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains with infinite residue fields in term…
The Ziegler spectrum of the ring of entire complex valued functions
Sonia L'Innocente, Francoise Point, Gena Puninski +1
We will describe the Ziegler spectrum of the ring of entire complex valued functions
Bézout domains and lattice-valued modules
Sonia L'Innocente, Françoise Point
Let B be a commutative Bézout domain B and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class of B-modules. We analyse the definable…
On the decidability of the theory of modules over the ring of algebraic integers
Sonia L'Innocente, Carlo Toffalori, Gena Puninski
We prove that the theory of all modules over the ring of algebraic integers is decidable.
Factorisation of germ-like series
Sonia L'Innocente, Vincenzo Mantova
A classical tool in the study of real closed fields are the fields of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $…