000131384 001__ 131384 000131384 005__ 20240208155436.0 000131384 0247_ $$2doi$$a10.1080/00927870903366918 000131384 0248_ $$2sideral$$a102659 000131384 037__ $$aART-2011-102659 000131384 041__ $$aeng 000131384 100__ $$0(orcid)0000-0002-6750-8971$$aMarco Buzunariz, Miguel Angel 000131384 245__ $$aGraded Betti Numbers of the Logarithmic Derivation Module 000131384 260__ $$c2011 000131384 5060_ $$aAccess copy available to the general public$$fUnrestricted 000131384 5203_ $$aLet Q ¿ x1 xn = S be a homogeneous polynomial of degree d. The freeness of the logarithmic derivation module, DQ, and of its natural generalizations has been widely studied. In the free case, DQ n i=1 S-di, where the di’s are the exponents of the module; and as a direct consequence of the Saito–Ziegler criterion, the formula d = i di holds. In this article, we give a generalization of this formula in the non-free case. Moreover, we show that an equivalent formula is also true in the quasi-homogeneous case, and show to what extent it can be generalized for arbitrary polynomials. 000131384 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E15 000131384 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000131384 590__ $$a0.347$$b2011 000131384 591__ $$aMATHEMATICS$$b235 / 289 = 0.813$$c2011$$dQ4$$eT3 000131384 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000131384 700__ $$0(orcid)0000-0002-6559-4722$$aMartin-Morales, Jorge 000131384 773__ $$g38, 11 (2011), 4348-4361$$pCommun. Algebra$$tCOMMUNICATIONS IN ALGEBRA$$x0092-7872 000131384 8564_ $$s234658$$uhttps://zaguan.unizar.es/record/131384/files/texto_completo.pdf$$yPostprint 000131384 8564_ $$s1329663$$uhttps://zaguan.unizar.es/record/131384/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000131384 909CO $$ooai:zaguan.unizar.es:131384$$particulos$$pdriver 000131384 951__ $$a2024-02-08-14:37:40 000131384 980__ $$aARTICLE