# Biorthogonality in $\mathcal A$-Pairings and Hyperbolic Decomposition Theorem for $\mathcal A$-Modules

Mathematics – Rings and Algebras

Scientific paper

[ 0.00 ] – not rated yet Voters 0   Comments 0

## Details Biorthogonality in $\mathcal A$-Pairings and Hyperbolic Decomposition Theorem for $\mathcal A$-Modules Biorthogonality in $\mathcal A$-Pairings and Hyperbolic Decomposition Theorem for $\mathcal A$-Modules

30 pages

Scientific paper

In this paper, as part of a project initiated by A. Mallios consisting of exploring new horizons for \textit{Abstract Differential Geometry} ($\grave{a}$ la Mallios), \cite{mallios1997, mallios, malliosvolume2, modern}, such as those related to the \textit{classical symplectic geometry}, we show that results pertaining to biorthogonality in pairings of vector spaces do hold for biorthogonality in pairings of $\mathcal A$-modules. However, for the \textit{dimension formula} the algebra sheaf $\mathcal A$ is assumed to be a PID. The dimension formula relates the rank of an $\mathcal A$-morphism and the dimension of the kernel (sheaf) of the same $\mathcal A$-morphism with the dimension of the source free $\mathcal A$-module of the $\mathcal A$-morphism concerned. Also, in order to obtain an analog of the Witt's hyperbolic decomposition theorem, $\mathcal A$ is assumed to be a PID while topological spaces on which $\mathcal A$-modules are defined are assumed \textit{connected}.

No associations

LandOfFree

## Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

## Rating

Biorthogonality in $\mathcal A$-Pairings and Hyperbolic Decomposition Theorem for $\mathcal A$-Modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Biorthogonality in $\mathcal A$-Pairings and Hyperbolic Decomposition Theorem for $\mathcal A$-Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Biorthogonality in $\mathcal A$-Pairings and Hyperbolic Decomposition Theorem for $\mathcal A$-Modules will most certainly appreciate the feedback.

Profile ID: LFWR-SCP-O-51196

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.