In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right division algorithm and generate a right version of Buchberger algorithm over bijective skew PBW extensions, finally we illustrate some examples using the SPBWE.lib library implemented in Maple (see [1], [4]). It is important to note that the development of this theory is fundamental to complete the SPBWE.lib library and to be able to develop many of the homological applications that arise as result of obtaining the right Gr\"obner bases over skew PBW extensions. Comment: [1] Fajardo, W., A computational Maple library for skew PBW extensions, Fundamenta Informaticae, 176, 2019, 159-191. [3] Fajardo, W., Gallego, C., Lezama, O., Reyes, A., Suarez, H., Vanegas, H., Skew PBW extensions, ISBN 978-3-030-53377-9, Springer Switzerland AG 2020. [4] Fajardo, W, Extended modules over skew PBW extensions, Ph.D. Thesis, Universidad Nacional de Colombia, Bogot\'a, 2018

In this paper we present a computational package developed for making computations involved in many homological applications of the Grbner theory of skew PBW extensions.

In this short note we present an elementary matrix-constructive algorithmic proof of the Quillen-Suslin theorem for Ore extensions A := K[ x; σ, δ], where K is a division ring, σ : K → K is a division ring automorphism and σ : K → K is a σ-derivation of K. It asserts that every finitely generated projective A-module is free. We construct a symbolic algorithm that computes the basis of a given finitely generated projective A-module. The algorithm is implemented in a computational package. Its efficiency is illustrated by four representative examples.