Modules with cosupport and injective functors

Details Modules with cosupport and injective functors Modules with cosupport and injective functors

2008-07-22

arxiv.org/abs/0807.3499v1

Mathematics

Rings and Algebras

16 pages

Scientific paper

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 (B^{op},Ab). In this paper, we study the category (Mod-R)^B of modules with cosupport in B. We show that (Mod-R)^B 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-Hugel, Enochs, Krause, Rada, and Saorin 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-R)^B. Our applications include a generalization of a result by Gruson-Jensen and Enochs on pure injective envelopes of flat modules.

Affiliated with

Also associated with

No associations

Rating

Modules with cosupport and injective functors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modules with cosupport and injective functors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modules with cosupport and injective functors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-436362