Ntumba, Patrice P.2014-10-022014-04Patrice P. Ntumba (2014) Reflexivity of orthogonality in A-modules, Quaestiones Mathematicae, 37:2, 231-247, DOI: 10.2989/16073606.2013.779992.0379-9468 (print)1727-933X (online)10.2989/16073606.2013.779992http://hdl.handle.net/2263/42203In this paper, as part of a project initiated by A. Mallios consisting of exploring new horizons for Abstract Differential Geometry (`a la Mallios), [5, 6, 7, 8], such as those related to the classical symplectic geometry, we show that essential results pertaining to biorthogonality in pairings of vector spaces do hold for biorthogonality in pairings of A-modules. We single out that orthogonality is reflexive for orthogonally convenient pairings of free A-modules of finite rank, governed by non-degenerate A-morphisms, and where A is a PID (Corollary 3.8). For the rank formula (Corollary 3.3), the algebra sheaf A is assumed to be a PID. The rank formula relates the rank of an A-morphism and the rank of the kernel (sheaf) of the same A-morphism with the rank of the source free A-module of the A-morphism concerned.en© 2014 NISC (Pty) Ltd. Taylor and Francis. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 37, no. 2, pp.231-247, 2014. doi : 10.2989/16073606.2013.779992. Quaestiones Mathematicae is available online at : http://www.tandfonline.com/loi/tqma20.Convenient A-modulesQuotient A-modulesFree subpresheafOrthogonally convenient A-pairingsPostprint Article