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Homological differences between finite and infinite dimensional representations of algebras. (English) Zbl 0991.16002

Krause, Henning (ed.) et al., Infinite length modules. Proceedings of the conference, Bielefeld, Germany, September 7-11, 1998. Basel: Birkhäuser. Trends in Mathematics. 425-439 (2000).
This is a nice survey on the state of the art of the finitistic dimension conjectures for finite dimensional algebras. After a brief historical account on these conjectures, the author recalls his examples showing that the difference between the little and the big finitistic projective dimension can be as large as possible. The main part of the paper, however, is devoted to discuss results on these conjectures related to the notion of contravariant finiteness of the subcategory of the modules of finite projective dimension.
For the entire collection see [Zbl 0945.00021].

MSC:

16E10 Homological dimension in associative algebras
16G10 Representations of associative Artinian rings
16G30 Representations of orders, lattices, algebras over commutative rings
16D90 Module categories in associative algebras
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