doi:10.1080/00927870903366918engMarco Buzunariz, Miguel AngelMartin-Morales, JorgeGraded Betti Numbers of the Logarithmic Derivation ModuleART-2011-102659Let Q ¿ x1 xn = S be a homogeneous polynomial of degree d. The freeness of the logarithmic derivation module, DQ, and of its natural generalizations has been widely studied. In the free case, DQ n i=1 S-di, where the di’s are the exponents of the module; and as a direct consequence of the Saito–Ziegler criterion, the formula d = i di holds. In this article, we give a generalization of this formula in the non-free case. Moreover, we show that an equivalent formula is also true in the quasi-homogeneous case, and show to what extent it can be generalized for arbitrary polynomials.2011http://zaguan.unizar.es/record/13138410.1080/00927870903366918http://zaguan.unizar.es/record/131384oai:zaguan.unizar.es:131384info:eu-repo/grantAgreement/ES/DGA/E15COMMUNICATIONS IN ALGEBRA 38, 11 (2011), 4348-4361by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess