Geodesic
On a Theorem of Burgess and Stephenson
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 603-605

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

A theorem of Burgess and Stephenson asserts that in an exchange ring with central idempotents, every maximal left ideal is also a right ideal. The proof uses sheaf-theoretic techniques. In this paper, we give a short elementary proof of this important theorem.
DOI : 10.4153/S0008439518000619
Mots-clés : exchange ring, abelian ring, left quasi-duo ring 
On a Theorem of Burgess and Stephenson. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 603-605. doi: 10.4153/S0008439518000619
@misc{10_4153_S0008439518000619,
     title = {On a {Theorem} of {Burgess} and {Stephenson}},
     journal = {Canadian mathematical bulletin},
     pages = {603--605},
     year = {2019},
     volume = {62},
     number = {3},
     doi = {10.4153/S0008439518000619},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000619/}
}
TY  - JOUR
TI  - On a Theorem of Burgess and Stephenson
JO  - Canadian mathematical bulletin
PY  - 2019
SP  - 603
EP  - 605
VL  - 62
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000619/
DO  - 10.4153/S0008439518000619
ID  - 10_4153_S0008439518000619
ER  - 
%0 Journal Article
%T On a Theorem of Burgess and Stephenson
%J Canadian mathematical bulletin
%D 2019
%P 603-605
%V 62
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000619/
%R 10.4153/S0008439518000619
%F 10_4153_S0008439518000619

[1] Burgess, W. and Stephenson, W., Rings all of whose Pierce stalks are local . Canad. Math. Bull. 22(1979), 159–164. . Google Scholar | DOI

[2] Crawley, P. and Jónsson, B., Refinements for infinite direct decompositions of algebraic systems . Pacific J. Math. 14(1964), 797–855. Google Scholar

[3] Feller, E. H., Properties of primary noncommutative rings . Trans. Amer. Math. Soc. 89(1958), 79–91. . Google Scholar | DOI

[4] Huh, C., Jang, S. H., Kim, C. O., and Lee, Y., Rings whose maximal one-sided ideals are two-sided . Bull. Korean Math. Soc. 39(2002), 411–422. . Google Scholar | DOI

[5] Lam, T. Y. and Dugas, A. S., Quasi-duo rings and stable range descent . J. Pure and Appl. Algebra 195(2005), 243–259. . Google Scholar | DOI

[6] Nicholson, W. K., Lifting idempotents and exchange rings . Trans. Amer. Math. Soc. 229(1977), 269–278. . Google Scholar | DOI

[7] Warfield, R., Exchange rings and decompositions of modules . Math. Ann. 199(1972), 31–36. . Google Scholar | DOI

[8] Yu, H.-P., On quasi-duo rings . Glasgow Math. J. 37(1995), 21–31. . Google Scholar | DOI

Cité par Sources :