2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149969We prove the algebraicity of smooth $CR$-mappings between algebraic Cauchy--Riemann manifolds. A generalization of separate algebraicity principle is established.AMS-TeX, 14 pagesAlgebraic GeometryOn $CR$ mappings between algebraic Cauchy--Riemann manifolds and separate algebraicity for holomorphic functionstext