Geodesic
Finite principal ideal rings
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 364-382 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1973_20_3_a3,
     author = {A. A. Nechaev},
     title = {Finite principal ideal rings},
     journal = {Sbornik. Mathematics},
     pages = {364--382},
     year = {1973},
     volume = {20},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_20_3_a3/}
}
TY  - JOUR
AU  - A. A. Nechaev
TI  - Finite principal ideal rings
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 364
EP  - 382
VL  - 20
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1973_20_3_a3/
LA  - en
ID  - SM_1973_20_3_a3
ER  - 
%0 Journal Article
%A A. A. Nechaev
%T Finite principal ideal rings
%J Sbornik. Mathematics
%D 1973
%P 364-382
%V 20
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1973_20_3_a3/
%G en
%F SM_1973_20_3_a3
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/

[1] A. V. Jategaonkar, Left principal ideal. rings, Lecture Notes in math., 123, 1970 | MR | Zbl

[2] L. A. Skornyakov, “Tsepnye sleva koltsa”, Sb. pamyati N. G. Chebotareva, Kazansk. un-t, 1964, 75–88

[3] R. Radhgavendran, “Finite associative rings”, Compositio math., 21:2 (1969), 195–229 | MR

[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