2012/01/27 by Maryam Salimi, Salimi, Maryam, Sean Sather-Wagstaff +5
Mathematics · #13D02 #13D05 #13D07 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D02 #msc:13D05 #msc:13D07
paper · pdf · doi:10.48550/arxiv.1201.5869
29 pages
arxiv created 2012/01/27 · arxiv updated 2012/01/30
We consider relative Tor functors built from resolutions described by a semidualizing module C over a commutative noetherian ring R. We show that the bifunctors TorFCMi (-,-) and TorPCMi (-,-), defined using flat-like and projective-like resolutions, are isomorphic. We show how the vanishing of these functors characterizes the finiteness of the homological dimension FC-pd, and we use this to give a relation between the FC-pd of a given module and that of a pure submodule. On the other hand, we show that other relations that one may expect to hold similarly, fail in general. In fact, such relations force the semidualizing modules under consideration to be trivial.