2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129699This paper extends the construction of invariants for virtual knots to virtual long knots and introduces two new invariant modules of virtual long knots. Several interesting features are described that distinguish virtual long knots from their classical counterparts with respect to their symmetries and the concatenation product.14 pages 11 figuresGeometric TopologyRings and Algebras57M27text