The Galois ring GR(p,m) of characteristic p and cardinality p, where p is a prime and r,m ≥ 1 are integers, is a Galois extension of the residue class ring Zpr by a root ω of a monic basic irreducible polynomial of degree m over Zpr . Every element of GR(p ,m) can be expressed uniquely as a polynomial in ω with coefficients in Zpr and degree less than or equal to m − 1, thus GR(p,m) is a free m...
