Interpretation functors which are full on pure-injective modules with applications to R-torsion-free modules over R-orders

Gregory, Lorna ORCID: https://orcid.org/0000-0002-5508-7217 (2026) Interpretation functors which are full on pure-injective modules with applications to R-torsion-free modules over R-orders. Representation Theory, 30 (7). pp. 175-195. ISSN 1088-4165

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Abstract

Let R,S be rings, ⊆ mod−R a covariantly finite subcategory, the smallest definable subcategory of Mod-R containing and a definable subcategory of Mod-S. We show that if I:⟶ is an interpretation functor such that I ⊆ mod-S and whose restriction to 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.

Item Type:	Article
Uncontrolled Keywords:	bäackstroäm orders,orders over a dvr,ziegler spectrum,interpretation functor,pure-injective,mathematics (miscellaneous) ,/dk/atira/pure/subjectarea/asjc/2600/2601
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	https://www.scopus.com/pages/publication...
Depositing User:	LivePure Connector
Date Deposited:	05 Jan 2026 16:30
Last Modified:	06 Oct 2026 09:45
URI:	https://ueaeprints.uea.ac.uk/id/eprint/101522
DOI:	10.1090/ert/711

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