Geodesic
On the Galois Theory of Commutative Rings II: Automorphisms induced in Residue Rings
Canadian journal of mathematics, Tome 39 (1987) no. 5, pp. 1025-1037

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

Let G be a group of automorphisms of a commutative ring K, and let KG denote the Galois subring consisting of all elements left fixed by every g in G. An ideal M is G-stable, or G-invariant, provided that g(x) lies in M for every x in M, that is, g(M) ⊆ M, for every g in G. Then, every g in G induces an automorphism in the residue ring , and if is the group consisting of all , trivially 1 When the inclusion (1) is strict, then G is said to be cleft at M, or by M, and otherwise G is uncleft at (by) M. When G is cleft at all ideals except 0, then G is cleft, and uncleft otherwise. 
Faith, Carl. On the Galois Theory of Commutative Rings II: Automorphisms induced in Residue Rings. Canadian journal of mathematics, Tome 39 (1987) no. 5, pp. 1025-1037. doi: 10.4153/CJM-1987-052-9
@article{10_4153_CJM_1987_052_9,
     author = {Faith, Carl},
     title = {On the {Galois} {Theory} of {Commutative} {Rings} {II:} {Automorphisms} induced in {Residue} {Rings}},
     journal = {Canadian journal of mathematics},
     pages = {1025--1037},
     year = {1987},
     volume = {39},
     number = {5},
     doi = {10.4153/CJM-1987-052-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-052-9/}
}
TY  - JOUR
AU  - Faith, Carl
TI  - On the Galois Theory of Commutative Rings II: Automorphisms induced in Residue Rings
JO  - Canadian journal of mathematics
PY  - 1987
SP  - 1025
EP  - 1037
VL  - 39
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-052-9/
DO  - 10.4153/CJM-1987-052-9
ID  - 10_4153_CJM_1987_052_9
ER  - 
%0 Journal Article
%A Faith, Carl
%T On the Galois Theory of Commutative Rings II: Automorphisms induced in Residue Rings
%J Canadian journal of mathematics
%D 1987
%P 1025-1037
%V 39
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-052-9/
%R 10.4153/CJM-1987-052-9
%F 10_4153_CJM_1987_052_9

[1] 1. Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409. Google Scholar

[2] 2. Chase, S. U., Harrison, D. K. and Rosenberg, A., Galois theory and Galois cohomology of commutative rings, Memoirs A.M.S. 52 (1965), 15–33. Google Scholar

[3] 3. DeMeyer, F. and Ingraham, E., Separable algebras over commutative rings, Lecture Notes in Math. 181 (Springer-Verlag, Berlin, Heidelberg and New York, 1971). Google Scholar | DOI

[4] 4. Faith, C., Galois extensions of commutative rings, Math. J. Okayama U. 18 (1976), 113–116. Google Scholar

[5] 5. Faith, C., On the Galois theory of commutative rings I: Dedekind's theorem on the independence of automorphisms revisited, in Algebraist's Hommage, Proceedings of the Yale Symposium in honor of Nathan Jacobson, New Haven (1981), Contemporary Math. 73(1982), 183–192. Google Scholar

[6] 6. Faith, C., Algebra II: Ring theory, (Springer-Verlag, 1976). Google Scholar | DOI

[7] 7. Kaplansky, I., A theorem on division rings, Can. J. Math. 3 (1951), 290–292. Google Scholar

[8] 8. Shamsuddin, A., Rings with automorphisms leaving no nontrivial proper ideals invariant, Proceedings of the Conference on Algebra and Geometry, Kuwait University, Khaldiya, Kuwait. Google Scholar | DOI

[9] 9. Vasconcelos, W., On local and stable cancellation, An. Acad. Brasil, Ci 37 (1965), 389–393. Google Scholar

[10] 10. Vasconcelos, W., On finitely generated flat modules, Trans. A.M.S. 138 (1969), 505–512. Google Scholar

[11] 11. Vasconcelos, W., Injective endomorphisms of finitely generated modules, Proc. A.M.S. 25 (1970), 900–901. Google Scholar

Cité par Sources :