Geodesic
Finite principal ideal rings
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 364-382 
A. A. Nechaev. Finite principal ideal rings. Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 364-382. http://geodesic.mathdoc.fr/item/SM_1973_20_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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[4] A. A. Nechaev, “O stroenii konechnykh kolets”, Matem. zametki, 10:6 (1971), 679–688 | Zbl

[5] J. Brawely Jr., “Similar involutory matrices”, Amer. Math. Month., 73:5 (1966), 499–501 | DOI | MR

[6] M. Nagata, “Local rings”, Int. tracts in pure and appl. math., no. 13, New-York, 1962 | MR

[7] N. Burbaki, Kommutativnaya algebra, izd-vo «Mir», Moskva, 1971 | MR

[8] S. Leng, Algebra, izd-vo «Mir», Moskva, 1968

[9] S. Leng, Algebraicheskie chisla, izd-vo «Mir», Moskva, 1966 | MR

[10] F. R. Gantmakher, Teoriya matrits, izd-vo «Nauka», Moskva, 1966 | MR