Finite Principal Ideal Rings
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 277-283

Voir la notice de l'article provenant de la source Cambridge University Press

This paper determines the structure of finite rings whose two sided ideals are principal as left ideals, and as right ideals. Such rings will be called principal ideal rings. Although finite rings have been studied extensively [1], [5], [12], [14] and the tools necessary for describing finite principal ideal rings have been available for thirty years, these structure theorems (which are essentially given in a more general setting in [4]) seem to have been overlooked. In particular, let or be an endomorphism of a ring V.
Fisher, James L. Finite Principal Ideal Rings. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 277-283. doi: 10.4153/CMB-1976-043-1
@article{10_4153_CMB_1976_043_1,
     author = {Fisher, James L.},
     title = {Finite {Principal} {Ideal} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {277--283},
     year = {1976},
     volume = {19},
     number = {3},
     doi = {10.4153/CMB-1976-043-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-043-1/}
}
TY  - JOUR
AU  - Fisher, James L.
TI  - Finite Principal Ideal Rings
JO  - Canadian mathematical bulletin
PY  - 1976
SP  - 277
EP  - 283
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-043-1/
DO  - 10.4153/CMB-1976-043-1
ID  - 10_4153_CMB_1976_043_1
ER  - 
%0 Journal Article
%A Fisher, James L.
%T Finite Principal Ideal Rings
%J Canadian mathematical bulletin
%D 1976
%P 277-283
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-043-1/
%R 10.4153/CMB-1976-043-1
%F 10_4153_CMB_1976_043_1

[0] 0. Atiyah, M. F. and Macdonald, I. G., Introduction to Commutative Algebra, Addison-Wesley, 1969. Google Scholar

[1] 1. Clark, W. E., A coefficient ring for finite non-commutative rings, Proc. Amer. Math. Soc. 33 (1972), 25–28. Google Scholar

[2] 2. Clark, W. E. and Drake, D. A., Finity chain rings, Abh. Math. Sem. Univ. Hamburg 39 (1973) 147–153. Google Scholar

[3] 3. Cohen, I. S., On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54–106. Google Scholar

[4] 4. Fisher, J. L., Structure theorems for non-commutative complete local rings, Thesis, Calif. Inst, of Tech., 1969. Google Scholar

[5] 5. Fountain, J. B., Nilpotent principal ideal rings, Proc. London Math. Soc. 20 (1970), 348–364. Google Scholar

[6] 6. Hochschild, G., Double vector spaces over division rings, Amer. J. of Math. 71 (1949), 443–460. Google Scholar

[7] 7. Hungerford, T. W., On the structure of principal ideal rings, Pacific J. of Math. 25 (1968), 543–547. Google Scholar

[8] 8. Jacobson, N., An extension of Galois theory to non-normal and non-separable fields, Amer. J. of Math. 66 (1944), 1–29. Google Scholar

[9] 9. Jacobson, N., The theory of rings, Math. Surveys II, Amer. Math. Soc, 1943. Google Scholar

[10] 10. Jategaonkar, A. V., Left principal ideal rings, Lecture Notes in Math. 123 (1970), Springer Verlag. Google Scholar

[11] 11. McLean, K. R., Commutative artinian principal ideal rings, Proc. London Math. Soc. 26 (1973), 249–272. Google Scholar

[12] 12. Raghavendran, R., Finite associative rings, Compositio Math. 21 (1969), 195–229. Google Scholar

[13] 13. Rowen, L. H., Some results on the center of a ring with polynomial identity, Bull. Amer. Math. Soc. 79 (1973), 219–223. Google Scholar

[14] 14. Wilson, R. S., On the structure of finite rings, Compositio Math. 26 (1973), 79–93. Google Scholar

Cité par Sources :