9 papers
The lattice of abstract elementary classes of modules
Tapani Hyttinen, Marcos Mazari-Armida, Gianluca Paolini
Let be a ring. We organize the abstract elementary classes whose underlying class is the class of all -modules and whose strong submodel relation lies between the submodule…
Deconstructible classes of modules and stability
Marcos Mazari-Armida, Jan Trlifaj
We show that every deconstructible class of modules with all embeddings, all pure embedding and all RD-embeddings is stable. The argument is presented in the context of abstract cl…
Cofibrant generation of pure monomorphisms in presheaf categories
Sean Cox, Jonathan Feigert, Mark Kamsma +2
We characterise when the pure monomorphisms in a presheaf category are cofibrantly generated in terms of the category . In particular, when…
On the abstract elementary class of acts with embeddings
Marcos Mazari-Armida, JiÅà Rosický
We study the class of acts with embeddings as an abstract elementary class. We show that the class is always stable and show that superstability in the class is characterized algeb…
On the spectrum of limit models
Jeremy Beard, Marcos Mazari-Armida
We study the spectrum of limit models assuming the existence of a nicely behaved independence notion. Under reasonable assumptions, we show that all `long' limit models are isomorp…
On limit models and parametrized noetherian rings
Marcos Mazari-Armida
We study limit models in the abstract elementary class of modules with embeddings as algebraic objects. We characterize parametrized noetherian rings using the degree of injectivit…