2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98218This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.7 pages. Proc. Am. Math. Soc. (to appear)Commutative Algebra13C15; 13F20; 13F05; 13G05; 13B02; 13B30text