Finite principal ideal rings

Every such ring is a direct sum of matrix rings over finite completely primary principal ideal rings. These latter rings are called Galois–Eisenstein–Ore rings or GEO-rings.
A number of defining properties for GEO-rings are given, from which it follows that a finite ring with identity in which every two-sided ideal is left principal is a principal ideal ring.
A theorem on the existence of a distinguished basis in a fintie bimodule over a Galois ring is proved, generalizing a similar theorem of Raghavendran.
Finally, a GEO-ring is described as the quotient ring of an Ore polynomial ring over a Galois ring by an ideal of a special form, generated by Eisenstein polynomials.
Bibliography: 10 titles.