Takafumi Mase - A study on the domain independence of the Laurent property, the irreducibility and the coprimeness in lattice equations

ocnmp:13960 - Open Communications in Nonlinear Mathematical Physics, August 7, 2024, Volume 4 - https://doi.org/10.46298/ocnmp.13960
A study on the domain independence of the Laurent property, the irreducibility and the coprimeness in lattice equationsArticle

Authors: Takafumi Mase ORCID

    We study the Laurent property, the irreducibility and the coprimeness for lattice equations (partial difference equations), mainly focusing on how the choice of initial value problem (the choice of domain) affects these properties. We show that these properties do not depend on the choice of domain as long as they are considered together. In other words, these properties are inherent to a difference equation. Applying our result, we discuss the reductions of lattice equations. We show that any reduction of a Laurent system, even if the lattices have torsion elements, preserves the Laurent property.

    https://doi.org/10.46298/ocnmp.13960
    Source: arXiv.org:2406.16043
    Volume: Volume 4
    Published on: August 7, 2024
    Accepted on: August 2, 2024
    Submitted on: July 20, 2024
    Keywords: Mathematical Physics,Mathematics - Rings and Algebras,39A14 (Primary) 39A27, 13B30 (Secondary)
    Licence: arXiv.org - Non-exclusive license to distribute

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