On the Rank of Multi-graded Differential Modules
DeVries, Justin W.
arXiv, 1011.2167 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2010-11-09
Classification:  Mathematics - Commutative Algebra,  13Dxx (Primary), 55Uxx (Secondary) 
@article{1011.2167,
     author = {DeVries, Justin W.},
     title = {On the Rank of Multi-graded Differential Modules},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1011.2167}
}

DeVries, Justin W. On the Rank of Multi-graded Differential Modules. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1011.2167/