On the Rank of Multi-graded Differential Modules

Details On the Rank of Multi-graded Differential Modules On the Rank of Multi-graded Differential Modules

2010-11-09

arxiv.org/abs/1011.2167v1

Mathematics

Commutative Algebra

15 pages

Scientific paper

A \mathbb{Z}^d-graded differential R-module is a \mathbb{Z}^d-graded R-module equipped with an endomorphism, \delta, that squares to zero. For R=k[x_1,...,x_d], this paper establishes a lower bound on the rank of such a differential module when the underlying R-module is free. We define the Betti number of a differential module and use it to show that when the homology H(D)=ker(\delta)/im(\delta) of D is non-zero and finite dimensional over k then there is an inequality rank_R D >= 2^d.

Affiliated with

Also associated with

No associations

Rating

On the Rank of Multi-graded Differential Modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Rank of Multi-graded Differential Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Rank of Multi-graded Differential Modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-494155