2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145007General properties of an Abelian connection in Fedosov deformation quantization are investigated. Definition and criterion of being a finite formal series for an Abelian connection are presented. A proof that in 2-dimensional (2-D) case the Abelian connection is an ifinite formal series is done.13 pages; new formulation of the criterion, when the Abelian connection is a finite formal series, is proposed. Modified proof of the fact, that on 2-D symplectic space the Abelian correction is an infinite formal series, is shown. The part devoted to different symplectic connections generating the same Abelian correction, has been removed. It will be added to another paperMathematical Physics53C07;53D55text