In this paper we present new algorithms for non‐commutative Gröbner ready algebras, which enable one to perform advanced operations with ideals and modules. In spite of the big interest in algorithmic treatment of related problems, preimage of ideal and central character decomposition were not discussed before.

An important algotithm for computation of the kernel of a homomorphism of left modules is described in the form, optimized for performance. We present these algorithms together with their implementation in computer algebra system SINGULAR:PLURAL and detailed applications.