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.

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