Reflexivity of orthogonality in A-modules
Loading...
Date
Authors
Ntumba, Patrice P.
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor and Francis
Abstract
In 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.
Description
Keywords
Convenient A-modules, Quotient A-modules, Free subpresheaf, Orthogonally convenient A-pairings
Sustainable Development Goals
Citation
Patrice P. Ntumba (2014) Reflexivity of orthogonality in A-modules, Quaestiones Mathematicae, 37:2, 231-247, DOI: 10.2989/16073606.2013.779992.