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Bibliographic Details
Main Authors: Głoch, Filip, Kędzierski, Dawid E., Krasoń, Piotr
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2408.08207
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Table of Contents:
  • In \cite{kk04} the second and third author extended the methods of \cite{pr} and determined the \tm module structure on $\Ext^1(Φ,Ψ)$ where $Φ$ and $Ψ$ were Anderson \tm modules over $A={\mathbf F}_q[t]$ of some specific types. This approach involved the concept of biderivation and certain reduction algorithm. In this paper we generalize the results of \cite{pr} and \cite{kk04} and present complete algorithm for computation of \tm module structure on $\Ext^1(Φ,Ψ)$ for \tm modules $Φ$ and $Ψ$ such that $\rk Φ> \rk Ψ.$ The last condition is not sufficient for our algorithm to be executable. We show that it can be applied when the matrix at the biggest power of $τ$ in $Φ_t$ is invertible. We also introduce a notion of $τ$-composition series which we find suitable for the additive category of \tm modules and show that under certain assumptions on the composition series of $Φ$ and $Ψ$ our algorithm is also executable.