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.
