Ntumba, Patrice P.2015-09-282015-09-282014-04Ntumba, PP 2014, 'On the group sheaf of A-symplectomorphisms', Mathematica Slovaca, vol. 64, no. 4, pp. 843-858.0139-9918 (print)1337-2211 (online)10.2478/s12175-014-0243-5http://hdl.handle.net/2263/50066This is a part of a further undertaking to affirm that most of classical module theory may be retrieved in the framework of Abstract Differential Geometry (`a la Mallios). More precisely, within this article, we study some defining basic concepts of symplectic geometry on free A-modules by focussing in particular on the group sheaf of A-symplectomorphisms, where A is assumed to be a torsion-free PID C-algebra sheaf. The main result arising hereby is that A-symplectomorphisms locally are products of symplectic transvections, which is a particularly well-behaved counterpart of the classical result.en© 2014 Mathematical Institute Slovak Academy of Sciences. The original publication is available at : http://link.springer.comjournal/12175.Convenient A-modulePID C-algebra sheafSymplectic Gram-Schmidt theoremSymplectic A-transvectionsSymplectic group sheafSymplectic transvection group sheafPostprint Article