2007/01/30 by Hailong Dao, Dao, Hailong
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.math/0701884
arxiv created 2007/01/30 · arxiv updated 2009/12/01
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.