Intersection of Ideals with Non-commutative Subalgebras
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Computation of an intersection of a left ideal with a subalgebra, which is not fully investigated until now, is important for different areas of mathematics. We present an algorithm for the computation of the preimage of a left ideal under a morphism of non--commutative $GR$--algebras, and show both its abilities and limitations. The main computational tools are the elimination of variables by means of Gr\"obner bases together with the constructive treatment of opposite algebras and the utilization of a special bimodule structure.