2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218912We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symmetric implication algebra that has properties similar to cubic implication algebras and provide a representation of these algebras as subalgebras of a product of a cubic implication algebra and an implication algebra. We then show that every symmetric implication algebra is covered by a locally symmetric implication algebra.25 pagesCombinatoricsRings and Algebras06A12 (Primary), 08A30, 08A05 (Secondary)text