Abstract
Several authors have studied the filtered colimit closure lim→ B of a class B of finitely presented modules. Lenzing called lim B the category of modules with support in B, and proved that it is equivalent to the category of flat objects in the functor category (Bop, Ab) . In this paper, we study the category (Mod-RB) of modules with cosupport in B. We show that (Mod-RB) is equivalent to the category of injective objects in (B,Ab), and thus recover a classical result by Jensen-Lenzing on pure injective modules. Works of Angeleri-Hügel, Enochs, Krause, Rada, and Saorín make it easy to discuss covering and enveloping properties of (Mod-R) B, and furthermore we compare the naturally associated notions of B -coherence and B-noetherianness. Finally, we prove a number of stability results for lim B and (Mod-RB). Our applications include a generalization of a result by Gruson-Jensen and Enochs on pure injective envelopes of flat modules.
Original language | English |
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Journal | Algebras and Representation Theory |
Volume | 13 |
Issue number | 5 |
Pages (from-to) | 543-560 |
Number of pages | 18 |
ISSN | 1386-923X |
DOIs | |
Publication status | Published - Oct 2010 |