7 citations · 17 across the 11 of their papers we have counts for
11 papers
Interpretation functors which are full on pure-injective modules with applications to -torsion-free modules over -orders
Lorna Gregory
Let be rings, - a covariantly finite subcategory, the smallest definable subcategory of - containing $\mathca…
Dimensions on Lattice Ordered Abelian Groups and Model Theory of Modules over Prüfer Domains
Lorna Gregory
We prove a transfer theorem which, when combined with the Jaffard-Kaplansky-Ohm Theorem, allows results in model theory of modules over Bézout domains to be translated into results…
Decidability for the theory of modules over a Prüfer domain
Lorna Gregory
In this paper we give elementary conditions completely characterising when the theory of modules of a Prüfer domain is decidable. Using these results, we show that the theory of mo…
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…
Maranda's Theorem for Pure-Injective Modules and Duality
Lorna Gregory
Let be a discrete valuation domain with field of fractions and maximal ideal generated by . Let be an -order such that is a separable -algebra. Maranda sh…
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…
Ziegler Spectra of Serial Rings
Lorna Gregory, Gena Puninski
In this paper we prove that the Ziegler spectra of all serial rings are sober. We then use this proof to give a general framework for computing and understanding Ziegler spectra of…
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…
Ziegler closures of some unstable tubes
Lorna Gregory
We describe the modules in the Ziegler closure of ray and coray tubes in module categories over finite-dimensional algebras. We improve slightly on Krause's result for stable tubes…
Decidability of theories of modules over tubular algebras
Lorna Gregory
We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of…
Representation embeddings, interpretation functors and controlled wild algebras
Lorna Gregory, Mike Prest
We establish a number of results which say, roughly, that interpretation functors preserve algebraic complexity. First we show that representation embeddings between categories of…