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Summary: Infinite dimensional tilting theory
Lidia Angeleri H¨ugel
Universit`a dell'Insubria Varese, Italy
June 2008
Notation. Let R be a ring (associative, with 1),
Mod-R the category of all right R-modules,
mod-R the subcategory of all modules M admitting a projective
resolution
· · · Pk+1 Pk · · · P1 P0 M 0
where all Pi are finitely generated.
Definition. A module TR is called a tilting module provided
Definition. A module TR is called a tilting module provided
(T1) pdimT < ;
Definition. A module TR is called a tilting module provided
(T1) pdimT < ;
(T2) Exti
R (T, T(I)) = 0 for each i > 0 and all sets I;
Definition. A module TR is called a tilting module provided
(T1) pdimT < ;
(T2) Exti
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