2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132286The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains bounds for the Castelnuovo-Mumford regularity of the Rees algebra and for the Artin-Rees numbers.18 pagesCommutative Algebra13A30; 13B22text