Geodesic
FPF Rings and Some Conjectures of C. Faith
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 257-259

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

A left FPF ring is a ring R such that every finitely generated faithful left R -module generates the category of left R-modules. It is shown that such rings split into R = A⊕B, where A is a two sided ideal, and A contains the left singular ideal of R as an essential submodule. If R is FPF on both sides B is two sided too, and R is the product of A and B. An example shows this is the best possible and that right FPF does not imply left FPF.
DOI : 10.4153/CMB-1983-040-8
Mots-clés : 16A 48, 16A 36, Faithful generators, FPF, Singular ideal, self-injective rings 
Page, S. S. FPF Rings and Some Conjectures of C. Faith. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 257-259. doi: 10.4153/CMB-1983-040-8
@article{10_4153_CMB_1983_040_8,
     author = {Page, S. S.},
     title = {FPF {Rings} and {Some} {Conjectures} of {C.} {Faith}},
     journal = {Canadian mathematical bulletin},
     pages = {257--259},
     year = {1983},
     volume = {26},
     number = {3},
     doi = {10.4153/CMB-1983-040-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-040-8/}
}
TY  - JOUR
AU  - Page, S. S.
TI  - FPF Rings and Some Conjectures of C. Faith
JO  - Canadian mathematical bulletin
PY  - 1983
SP  - 257
EP  - 259
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-040-8/
DO  - 10.4153/CMB-1983-040-8
ID  - 10_4153_CMB_1983_040_8
ER  - 
%0 Journal Article
%A Page, S. S.
%T FPF Rings and Some Conjectures of C. Faith
%J Canadian mathematical bulletin
%D 1983
%P 257-259
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-040-8/
%R 10.4153/CMB-1983-040-8
%F 10_4153_CMB_1983_040_8

[1] 1. Azumaya, G., Completely faithful modules and self-injective rings, Nagoya Math. J. 27 (1966), 697-708. MR 35 #4253. Google Scholar

[2] 2. Faith, C., Injective quotient rings of commutative rings, Module Theory Lect. Notes in Math. 700, Springer-Verlag, Berlin, 151-203. Google Scholar

[3] 3. Faith, C., Results on the structure of FPF rings. To appear in Nagoya Math. Google Scholar

[4] 4. Lambek, J., Rings and Modules, Blaisdell, New York, 1966. Google Scholar

[5] 5. Osofsky, B., A generalization of quasi-Frobenius rings, J. Algebra, 4 (1966) 373-387. Google Scholar

[6] 6. Page, S., Regular FPF Rings, Pac. J. Math. Vol. 79, No. 1, 1978, 169-176. Google Scholar

[7] 7. Page, S., Semiprime and Nonsingular FPF rings. Comm. in Algebra, 10 #20 (1982). Google Scholar

[8] 8. Page, S., Semihereditary and Fully Idempotent FPF Rings. To appear in Comm. in Algebra. Google Scholar

[9] 9. Utumi, Y., On quotient rings, Osaka Math. J., 8 (1956), 1-18. Google Scholar

[10] 10. Utumi, Y., Self injective rings, J. Algebra, 6 (1967), 56-64. Google Scholar

Cité par Sources :