2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229657In modeling physical systems it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases, provide some basic properties and generalize a suitable variant of the Buchberger-Moeller algorithm as well as the AVI-algorithm to the subideal setting. The subideal version of the AVI-algorithm is then applied to an actual industrial problem.18 pages, 1 figureCommutative Algebra13P10text