In the new paper “**Comment on “new integrable family in n-dimensional homogeneous Lotka-Volterra systems with Abelian Lie Algebra” **[J. Phys. Soc. Jpn. 72 (2003) 973]” we present the new (generalized) Poisson structure and the Hamiltonian functions for the so-called generalized ladder system (GLS), obtaining also its first integrals as functionally independent Casimir functions for the associated Poisson algebra and thus proving the complete Liouville integrability of the GLS.

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