A finite ring with an identity whose lattice of ideals forms a unique chain is called ring. Let R be commutative invariants p,n,r,k,m. It known that Eisenstein extension degree k Galois S=GR(pn,r). If p−1 does not divide k, the structure unit group U(R) known. The case (p−1)∣k was partially considered by M. Luis (1991) providing counterexamples demonstrated results Ayoub failed to capture direc...