Ntumba, Patrice P.2011-08-082011-08-082010Ntumba, PP 2010, 'Witt's theorem in abstract geometric algebra', Ricerche di Matematica, vol. 59, no. 1, pp. 109-124.0035-5038 (print)1827-3491 (online)http://hdl.handle.net/2263/17027In an earlier paper of the author, a version of the Witt’s theorem was obtained within a specific subcategory of the category of A-modules: the full subcat-egory of convenient A-modules. A further investigation yields two more versions of the Witt’s theorem by revising the notion of convenient A-modules. For the first version, the A-bilinear form involved is either symmetric or antisymmetric, and the two isometric free sub-A-modules, the isometry between which may extend to an isom-etry of the non-isotropic convenient A-module concerned onto itself, are assumed pre-hyperbolic. On the other hand, for the second version, the A-bilinear form defined on the non-isotropic convenient A-module involved is set to be symmetric, and the two isometric free sub-A-modules, whose orthogonals are to be proved isometric, are assumed strongly non-isotropic and disjoint.en© Università degli Studi di Napoli "Federico II" 2011Sheaf of A-radicalsOrthosymmetric A-bilinear formsStrongly isotropic (non-isotropic) sub-A-modulesWeakly isotropic (non-isotropic) sub-A-modulesFree subpresheaves of modulesPre-hyperbolic free sub-A-modulesSheaf theoryAlgebra, AbstractPostprint Article