On liftable and weakly liftable modules

Details On liftable and weakly liftable modules On liftable and weakly liftable modules

2007-01-30

arxiv.org/abs/math/0701884v1

Mathematics

Commutative Algebra

Scientific paper

Let $T$ be a Noetherian ring and $f$ a nonzerodivisor on $T$. We study concrete necessary and sufficient conditions for a module over $R=T/(f)$ to be weakly liftable to $T$, in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over $T$ we define the loci for certain properties: liftable, weakly liftable, having finite projective dimension and study their relationships.

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