A criterion for primitive polynomials over Galois rings (Q5921703)

The authors provide a relationship between the representation of a root of a basic irreducible polynomial over a Galois ring and its order. They then present algebraic discriminants for primitive polynomials and sub-primitive polynomials. Using these results they give precise criteria for primitive polynomials over Galois rings with characteristic \(2^n\). They are also able to completely characterize trinomial and pentanomial primitive polynomials over \(\mathbb Z_{2^n}\).