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arXiv · 1807.11885

Inside factorial monoids and the cale monoid of a single Diophantine equation

Pedro A. García-Sánchez·Ulrich Krause·David Llena
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Abstract

We give a structure theorem for inside factorial domains. As an example we study the monoid of nonnegative integer solutions of equations of the form $a_1x_1+\cdots +a_{r-1}x_{r-1}=a_rx_r$, with $a_1,\ldots,a_r$ positive integers. This set is isomorphic to a simplicial full affine semigroup, and thus it can be described in terms of its extremal rays and the Ap\'ery sets with respect to the extremal rays.

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Pedro A. García-Sánchez, Ulrich Krause, David Llena. 2018-07-31. Inside factorial monoids and the cale monoid of a single Diophantine equation. https://arxiv.org/abs/1807.11885

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