2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110083We introduce and study the notion of $\star$-stability with respect to a semistar operation $\star$ defined on a domain $R$; in particular we consider the case where $\star$ is the $w$-operation. This notion allows us to generalize and improve several properties of stable domains and totally divisorial domains.21 pages. J. Pure Appl. Algebra, to appearCommutative Algebra13A15; 13F05; 13G05text