Relative Ext groups, resolutions, and Schanuel classes

Details Relative Ext groups, resolutions, and Schanuel classes Relative Ext groups, resolutions, and Schanuel classes

2006-10-27

arxiv.org/abs/math/0610844v1

Mathematics

Rings and Algebras

17 pages

Scientific paper

Given a precovering (also called contravariantly finite) class F there are three natural approaches to a homological dimension with respect to F: One based on Ext functors relative to F, one based on F-resolutions, and one based on Schanuel classes relative to F. In general these approaches do not give the same result. In this paper we study relations between the three approaches above, and we give necessary and sufficient conditions for them to agree.

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