Ntumba, Patrice P.Anyaegbunam, Adaeze Christiana2011-04-182011-04-182011Ntumba, PP & Anyaegbunam, AC 2011, 'A-transvections and Witt’s theorem in symplectic A-modules', Mediterranean Journal of Mathematics, doi:10.1007/s00009-010-0102-8. [http://www.springer.com/birkhauser/mathematics/journal/9]1660-5446 (print)1660-5454 (online)10.1007/s00009-010-0102-8http://hdl.handle.net/2263/16309Building on prior joint work by Mallios and Ntumba, we study transvections (J. Dieudonn´e), a theme already important from the classical theory, in the realm of Abstract Geometric Algebra, referring herewith to symplectic A-modules. A characterization of A-transvections, in terms of A-hyperplanes (Theorem 1.4), is given together with the associated matrix definition (Corollary 1.5). By taking the domain of coefficients A to be a PID-algebra sheaf, we also consider the analogue of a form of the classical Witt’s extension theorem, concerning A-symplectomorphisms defined on appropriate Lagrangian sub-A-modules (Theorem 2.3 and 2.4).en© Springer-Verlag 2010. The original publication is available at www.springerlink.com.A-homothecyA-hyperplaneA-transvectionA-transvection of classical typeTransvection matrixSymplectic A-modulePID-algebra sheafOrthogonally convenient pairingOrthogonalization methodsPostprint Article