Marcos Mazari-Armida

activity

20182020

collaborators

7 papers

math.GR2020

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 $λ$ such that there is a universal abelian $p$ -group for purity of cardinality $λ$ , i.e., an abelian $p$ -group $U_{λ}$ o…

math.LO2020

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. $T h eor e m$ : Let $K$ be an AEC with a monster model. - If $K$ has a…

math.LO2019

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. $Theorem.$ For a ring $R$ the following are e…

math.LO2019

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…

math.LO2019

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. $T h eor e m .$ Let $R$ be a ring, $T$ a first-order theory with an infinite model extendi…

math.LO2018

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…