Geodesic
A Note on Semihereditary Rings
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 439-440

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

It's well known (see Endo [1]) that for a commutative ring A, if A is semihereditary then w.gl. dim. A ≤ 1. It seems worth recording the noncommutative version of this. 
Enochs, E. A Note on Semihereditary Rings. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 439-440. doi: 10.4153/CMB-1973-070-2
@article{10_4153_CMB_1973_070_2,
     author = {Enochs, E.},
     title = {A {Note} on {Semihereditary} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {439--440},
     year = {1973},
     volume = {16},
     number = {3},
     doi = {10.4153/CMB-1973-070-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-070-2/}
}
TY  - JOUR
AU  - Enochs, E.
TI  - A Note on Semihereditary Rings
JO  - Canadian mathematical bulletin
PY  - 1973
SP  - 439
EP  - 440
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-070-2/
DO  - 10.4153/CMB-1973-070-2
ID  - 10_4153_CMB_1973_070_2
ER  - 
%0 Journal Article
%A Enochs, E.
%T A Note on Semihereditary Rings
%J Canadian mathematical bulletin
%D 1973
%P 439-440
%V 16
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-070-2/
%R 10.4153/CMB-1973-070-2
%F 10_4153_CMB_1973_070_2

[1] 1. Endo, S., On semihereditary rings, J. Math. Soc. Japan 13 (1961), 109–119. Google Scholar

[2] 2. Maddox, B. H., Absolutely pure modules, Proc. Amer. Math. Soc. 18 (1967), 155–158. Google Scholar

[3] 3. Cohn, P. M., On the free product of associative rings I, Math. Z. 71 (1959), 380–398. Google Scholar

[4] 4. Megibben, C., Absolutely pure modules, Proc. Amer. Math. Soc. 26 (1970), 561–566. Google Scholar

[5] 5. Lambek, J., A module is flat if and only if its character module is injective, Canad. Math. Bull. 7 (1964), 237–243. Google Scholar

Cité par Sources :