Geodesic
Injective endomorphisms and maximal left ideals of left Artinian rings
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 195-201

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

Given a ring R and an injective ring endomorphism α: R → R, not necessarily surjective, it is possible to define a minimal overring A(R, α) of R to which extends as an automorphism. The ring A(R, α) was first studied by D. A. Jordan in his paper [5], where he also introduces the central objects of this paper—the closed left ideals of R. As can be seen from Theorem 4.7 of [5], the left ideal structure of A(R, α) depends very strongly on the closed left ideals of R, and our aim here is to show that each maximal left ideal of a left Artinian ring is closed. 
Wilkinson, J. C. Injective endomorphisms and maximal left ideals of left Artinian rings. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 195-201. doi: 10.1017/S0017089500007229
@article{10_1017_S0017089500007229,
     author = {Wilkinson, J. C.},
     title = {Injective endomorphisms and maximal left ideals of left {Artinian} rings},
     journal = {Glasgow mathematical journal},
     pages = {195--201},
     year = {1988},
     volume = {30},
     number = {2},
     doi = {10.1017/S0017089500007229},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007229/}
}
TY  - JOUR
AU  - Wilkinson, J. C.
TI  - Injective endomorphisms and maximal left ideals of left Artinian rings
JO  - Glasgow mathematical journal
PY  - 1988
SP  - 195
EP  - 201
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007229/
DO  - 10.1017/S0017089500007229
ID  - 10_1017_S0017089500007229
ER  - 
%0 Journal Article
%A Wilkinson, J. C.
%T Injective endomorphisms and maximal left ideals of left Artinian rings
%J Glasgow mathematical journal
%D 1988
%P 195-201
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007229/
%R 10.1017/S0017089500007229
%F 10_1017_S0017089500007229

[1] 1.Cauchon, G. and Robson, J. C., Endomorphisms, derivations and polynomial rings, J. Alg. 53 (1978), 227–238. Google Scholar

[2] 2.Goldie, A. W., Rings with maximum condition, multigraphed notes (Yale University, 1961). Google Scholar

[3] 3.Jacobson, N., Structure of rings (Amer. Math. Soc., 1964). Google Scholar

[4] 4.Jategaonkar, A. V., Skew polynomial rings over orders in Artinian rings, J. Alg. 21 (1972), 51–59. Google Scholar

[5] 5.Jordan, D. A., Bijective extensions of injective ring endomorphisms, J. London Math. Soc. (2) 35 (1982), 435–448. Google Scholar

[6] 6.Wilkinson, J. C., Ph.D. thesis (University of Warwick, 1983). Google Scholar

Cité par Sources :