8 citations · 12 across the 12 of their papers we have counts for
19 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, Jiří 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 Stability and Existence of Models in Abstract Elementary Classes
Marcos Mazari-Armida, Sebastien Vasey, Wentao Yang
For an abstract elementary class and a cardinal , we prove under mild cardinal arithmetic assumptions, categoricity in two succesive cardinals, a…
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…
Building models in small cardinals in local abstract elementary classes
Marcos Mazari-Armida, Wentao Yang
There are many results in the literature where superstablity-like independence notions, without any categoricity assumptions, have been used to show the existence of larger models.…
Relative injective modules, superstability and noetherian categories
Marcos Mazari-Armida, Jiri Rosicky
We study classes of modules closed under direct sums, -submodules and -epimorphic images where is either the class of embeddings, -embed…
A note on torsion modules with pure embeddings
Marcos Mazari-Armida
We study Martsinkovsky-Russell torsion modules [MaRu20] with pure embeddings as an abstract elementary class. We give a model-theoretic characterization of the pure-injective and t…
Some stable non-elementary classes of modules
Marcos Mazari-Armida
Fisher [Fis75] and Baur [Bau75] showed independently in the seventies that if is a complete first-order theory extending the theory of modules, then the class of models of …
A model theoretic solution to a problem of László Fuchs
Marcos Mazari-Armida
Problem 5.1 in page 181 of [Fuc15] asks to find the cardinals such that there is a universal abelian -group for purity of cardinality , i.e., an abelian -group o…
Simple-like independence relations in abstract elementary classes
Rami Grossberg, Marcos Mazari-Armida
We introduce and study simple and supersimple independence relations in the context of AECs with a monster model. : Let be an AEC with a monster model. - If has a…
On superstability in the class of flat modules and perfect rings
Marcos Mazari-Armida
We obtain a characterization of left perfect rings via superstability of the class of flat left modules with pure embeddings. For a ring the following are e…
Superstability, noetherian rings and pure-semisimple rings
Marcos Mazari-Armida
We uncover a connection between the model-theoretic notion of superstability and that of noetherian rings and pure-semisimple rings. We characterize noetherian rings via superstabi…
On universal modules with pure embeddings
Thomas G. Kucera, Marcos Mazari-Armida
We show that certain classes of modules have universal models with respect to pure embeddings. Let be a ring, a first-order theory with an infinite model extendi…
Algebraic description of limit models in classes of abelian groups
Marcos Mazari-Armida
We study limit models in the class of abelian groups with the subgroup relation and in the class of torsion-free abelian groups with the pure subgroup relation. We show: $\textbf{T…
Non-forking w-good frames
Marcos Mazari Armida
We introduce the notion of a w-good -frame which is a weakening of Shelah's notion of a good -frame. Existence of a w-good -frame implies existence of a model of size $λ^{…
Universal classes near
Marcos Mazari-Armida, Sebastien Vasey
Shelah has provided sufficient conditions for an -sentence to have arbitrarily large models and for a Morley-like theorem to hold of . These conditions involve s…