2024/12/18 by Gregory, Lorna
#03C60 #03C98 #16G30 (primary) #16H2 #FOS: Mathematics #Logic (math.LO) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2412.13396
Let R,S be rings, X⊆ mod-R a covariantly finite subcategory, C the smallest definable subcategory of Mod-R containing X and D a definable subcategory of Mod-S. We show that if I:C→ D is an interpretation functor such that IX⊆ mod-S and whose restriction to X is full then I is full on pure-injective modules. We apply this theorem to an extension of a functor introduced by Ringel and Roggenkamp which, in particular, allows us to describe the torsion-free part of the Ziegler spectra of tame Bäckström orders. We also introduce the notion of a pseudogeneric module over an order which is intended to play the same role for lattices over orders as generic modules do for finite-dimensional modules over finite-dimensional algebras.