Geodesic
Twisted group rings which are semi-prime Goldie rings
Glasgow mathematical journal, Tome 16 (1975) no. 1, pp. 1-11

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

In this paper we examine when a twisted group ring, Rγ(G), has a semi-simple, artinian quotient ring. In §1 we assemble results and definitions concerning quotient rings, Ore sets and Goldie rings and then, in §2, we define Rγ(G). We prove a useful theorem for constructing a twisted group ring of a factor group and establish an analogue of a theorem of Passman. Twisted polynomial rings are discussed in §3 and I am indebted to the referee for informing me of the existence of [4]. These are used as a tool in proving results in §4. 
Reid, A. Twisted group rings which are semi-prime Goldie rings. Glasgow mathematical journal, Tome 16 (1975) no. 1, pp. 1-11. doi: 10.1017/S0017089500002433
@article{10_1017_S0017089500002433,
     author = {Reid, A.},
     title = {Twisted group rings which are semi-prime {Goldie} rings},
     journal = {Glasgow mathematical journal},
     pages = {1--11},
     year = {1975},
     volume = {16},
     number = {1},
     doi = {10.1017/S0017089500002433},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002433/}
}
TY  - JOUR
AU  - Reid, A.
TI  - Twisted group rings which are semi-prime Goldie rings
JO  - Glasgow mathematical journal
PY  - 1975
SP  - 1
EP  - 11
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002433/
DO  - 10.1017/S0017089500002433
ID  - 10_1017_S0017089500002433
ER  - 
%0 Journal Article
%A Reid, A.
%T Twisted group rings which are semi-prime Goldie rings
%J Glasgow mathematical journal
%D 1975
%P 1-11
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002433/
%R 10.1017/S0017089500002433
%F 10_1017_S0017089500002433

[1] 1.Connell, I. G., On the group ring, Canad. J. Math. 15 (1963), 650–685. Google Scholar | DOI

[2] 2.Goldie, A. W., Structure of noetherian rings, Lectures on rings and modules, Lecture Notes in Mathematics No. 246 (Springer-Verlag, 1972). Google Scholar

[3] 3.Herstein, I. N., Noncommutative rings, Cams Mathematical Monographs (Math. Assoc. of America, 1968). Google Scholar

[4] 4.Horn, A., Gruppenringe fastpolyzyklischer Gruppen und Ordnungen in Quasi-Frobenius-Ringen, Mitt. Math. Sent. Giessen 100 (1973). Google Scholar

[5] 5.Jennings, S. A., The group ring of a class of infinite nilpotent groups, Canad. J. Math. 7 (1955), 169–187. Google Scholar | DOI

[6] 6.Lambek, J., Lectures on rings and modules (Blaisdell, 1966). Google Scholar

[7] 7.Passman, D. S., Nil ideals in group rings, Mich. Math. J. 9 (1962), 375–384. Google Scholar | DOI

[8] 8.Passman, D. S., Radicals of twisted group rings, Proc. London Math. Soc. (3) 20 (1970), 409–437. Google Scholar | DOI

[9] 9.Passman, D. S., Radicals of twisted group rings II, Proc. London Math. Soc. (3) 22 (1971), 633–651. Google Scholar | DOI

[10] 10.Robinson, D. J. S., Finiteness conditions and generalised soluble groups, Parts 1, 2 Ergebnisse der Mathematik und ihrer Grenzgebiete Vol. 62, 63(Springer-Verlag, 1972). Google Scholar

[11] 11.Robson, J. C., Artinian quotient rings, Proc. London Math. Soc. (3) 17 (1972), 600–616. Google Scholar

[12] 12.Smith, P. F., Quotient rings of group rings, /. London Math. Soc. (2) 3 (1971), 645–660. Google Scholar | DOI

Cité par Sources :