Witt's theorem in abstract geometric algebra

Abstract

In 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.