Geodesic
Goldie criteria for some semiprime rings
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 297-308

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

We principally consider rings R of the form R = S[G], generated as a ring by the subring S of R and the subgroup G of the group of units of R normalizing S. (All our rings have identities except the nilrings.) We wish to deduce that certain semiprime images of R are Goldie rings from ring theoretic information about S and group theoretic information about G. Usually the latter is given in the form that G/N has some solubility or finiteness property, where N is some specified normal subgroup of G contained in S. Note we do not assume that N = G∩S; in particular N = 〈1〉 is always an option. 
Brown, K. A.; Wehrfritz, B. A. F. Goldie criteria for some semiprime rings. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 297-308. doi: 10.1017/S0017089500008363
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