Semilocal Group Algebras
Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 409-412.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $k[G]$ be a semilocal group algebra. It is shown that if $k$ is an algebraically closed field, then every finitely generated flat $k[G]$-module is projective.
@article{MZM_2005_78_3_a7,
     author = {M. F. Nasrutdinov},
     title = {Semilocal {Group} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {409--412},
     publisher = {mathdoc},
     volume = {78},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a7/}
}
TY  - JOUR
AU  - M. F. Nasrutdinov
TI  - Semilocal Group Algebras
JO  - Matematičeskie zametki
PY  - 2005
SP  - 409
EP  - 412
VL  - 78
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a7/
LA  - ru
ID  - MZM_2005_78_3_a7
ER  - 
%0 Journal Article
%A M. F. Nasrutdinov
%T Semilocal Group Algebras
%J Matematičeskie zametki
%D 2005
%P 409-412
%V 78
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a7/
%G ru
%F MZM_2005_78_3_a7
M. F. Nasrutdinov. Semilocal Group Algebras. Matematičeskie zametki, Tome 78 (2005) no. 3, pp. 409-412. http://geodesic.mathdoc.fr/item/MZM_2005_78_3_a7/

[1] Feis K., Algebra: koltsa, moduli i kategorii, T. 1, 1977; Т. 2, Мир, М., 1979 | MR

[2] Zalesskii A. E., Mikhalev A. V., “Gruppovye koltsa”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 2, VINITI, M., 1973, 5–118

[3] Bovdi A. A., Gruppovye koltsa, UMK VO, Kiev, 1988

[4] Bass H., “Finitistic dimension and a homological generalization of semi-primary rings”, Trans. Amer. Math. Soc., 95 (1960), 466–488 | DOI | MR

[5] Sakhaev I. I., Chirkov Ch. V., “Proektivnost konechno-porozhdennykh ploskikh modulei nad polulokalnym koltsom s edinstvennym primitivnym idealom”, Izv. vuzov. Matem., 1970, no. 6, 106 | MR | Zbl

[6] Puninski G., Rothmaler Ph., “When every finitely generated flat modules projective”, J. Algebra, 277 (2004), 542–558 | DOI | MR

[7] Jondrup S., “On finitely generated flat modules”, Math. Scand., 26 (1970), 233–240

[8] Sakhaev I. I., “O gruppe $K_0(A\Pi)$ dlya polulokalnykh kolets”, Math. Nachr., 130 (1987), 157–175 | DOI

[9] Sakhaev I. I., “O proektivnosti konechno porozhdennykh ploskikh modulei nad polulokalnymi koltsami”, Matem. zametki, 37:2 (1985), 152–162 | MR | Zbl

[10] Woods S. M., “On perfect group rings”, Proc. Amer. Math. Soc., 27:1 (1971), 49–52 | DOI

[11] Okninski J., “Spectrally finite and semilocal group rings”, Commun. Algebra, 8 (1980), 533–541 | DOI

[12] Zhuchin A. V., “O polulokalnykh polugruppovykh koltsakh”, Fundament. i prikl. matem., 5:1 (1999), 139–147

[13] Okninski J., “Semilocal skew group rings”, Proc. Amer. Math. Soc., 80:4 (1980), 552–554 | DOI

[14] Merzlyakov Yu. I., Ratsionalnye gruppy, Nauka, M., 1980