2019 Volume 71 Issue 2 Pages 515-554
Homological tilting modules of finite projective dimension are investigated. They generalize both classical and good tilting modules of projective dimension at most one, and produce recollements of derived module categories of rings in which generalized localizations of rings are involved. To decide whether a good tilting module is homological, a sufficient and necessary condition is presented in terms of the internal properties of the given tilting module. Consequently, a class of homological, non-trivial, infinitely generated tilting modules of higher projective dimension is constructed, and the first example of an infinitely generated 𝑛-tilting module which is not homological for each 𝑛 ≥ 2 is exhibited. To deal with both tilting and cotilting modules consistently, the notion of weak tilting modules is introduced. Thus similar results for infinitely generated cotilting modules of finite injective dimension are obtained, though dual technique does not work for infinite-dimensional modules.
This article cannot obtain the latest cited-by information.