2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69126We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger.4 pagesCommutative Algebra13P10text