2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222710Let $G$ be a reflection group acting on a vector space $V$ (over a field with zero characteristic). We denote by $S(V^*)$ the coordinate ring of $V$, by $M$ a finite dimensional $G$-module and by $χ$ a one-dimensional character of $G$. In this article, we define an algebra structure on the isotypic component associated to $χ$ of the algebra $S(V^*) \otimes Λ(M^*)$. This structure is then used to obtain various generalizations of usual criterions on regularity of integers.26 pagesGroup TheoryRings and Algebras13A50; 15A75text