2021/04/20 by Mazari-Armida, Marcos
#03C48. Secondary: 03C45 #03C60 #13L05 #FOS: Mathematics #Logic (math.LO) #Primary: 20K10 #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2104.10160
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 the Σ-pure-injective modules relative to the class of torsion modules assuming that the torsion submodule is a pure submodule. Our characterization of relative Σ-pure-injective modules strictly extends the classical charactetization of [GrJe76] and [Zim, 3.6]. We study the limit models of the class and determine when the class is superstable assuming that the torsion submodule is a pure submodule. As a corollary, we show that the class of torsion abelian groups with pure embeddings is strictly stable, i.e., stable not superstable.