Cotilting versus pure-injective modules

Francesca Mantese, Alberto Tonolo and Pavel Ruzicka

Vol. 212 (2003), No. 2, 321–332

DOI: 10.2140/pjm.2003.212.321

Abstract

Let R and S be arbitrary associative rings. A left R-module _RW is said to be cotilting if the class of modules cogenerated by _RW coincides with the class of modules for which the functor Ext_R¹(−,W) vanishes. In this paper we characterize the cotilting modules which are pure-injective. The two notions seem to be strictly connected: Indeed all the examples of cotilting modules known in the literature are pure-injective. We observe that if _RW_S is a pure-injective cotilting bimodule, both R and S are semiregular rings and we give a characterization of the reflexive modules in terms of a suitable “linear compactness” notion.

Milestones

Received: 8 January 2001

Revised: 7 January 2002

Published: 1 December 2003