From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: homological dimension of a module Date: 24 Nov 1997 14:45:15 GMT In article <347689C0.66@univ-rennes1.fr>, wrote: >Can you give me some examples of concrete computation of homological >dimension of a module and projective dimension. for example, Z/2Z as a >Z/4Z module. I'm not sure I've heard of the concept of "homological dimension of a module"; more precisely, if I heard it, I would translate it into "projective dimension". The latter is simply the length of the shortest projective resolution of the module. You're not likely to get good examples of the type you describe, since if M is a Z[G]-module, it can only have finite projective dimension if that dimension is at most 1, that is, M is either projective or the quotient of a projective module by a projective submodule. Equivalently, M is cohomologically trivial. This result is due to Rim. Certainly if G=Z/4Z and M=Z/2Z, we have H^i(G,M) = Z/2Z for all i, so this module is not cohomologically trivial; M has infinite projective dimension. dave