Reflexivity of orthogonality in A-modules

Show simple item record Ntumba, Patrice P. 2014-10-02T09:36:06Z 2014-04
dc.description.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. en_US
dc.description.embargo 2015-12-30
dc.description.librarian hb2014 en_US
dc.description.uri en_US
dc.identifier.citation Patrice P. Ntumba (2014) Reflexivity of orthogonality in A-modules, Quaestiones Mathematicae, 37:2, 231-247, DOI: 10.2989/16073606.2013.779992. en_US
dc.identifier.issn 0379-9468 (print)
dc.identifier.issn 1727-933X (online)
dc.identifier.other 10.2989/16073606.2013.779992
dc.language.iso en en_US
dc.publisher Taylor and Francis en_US
dc.rights © 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 : en_US
dc.subject Convenient A-modules en_US
dc.subject Quotient A-modules en_US
dc.subject Free subpresheaf en_US
dc.subject Orthogonally convenient A-pairings en_US
dc.title Reflexivity of orthogonality in A-modules en_US
dc.type Postprint Article en_US

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