2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105094We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings.8 pagesCommutative AlgebraRings and Algebras13A99text