A ring of quotients

Let be a radical filter in a ring R, and let the ring Q be defined by the equation Q= Hom_H (E, E), where H=Hom_R (E, E) and E is the -envelope of the ring. We show that the ring Q possesses the properties of a ring of quotients and coincides with the ring of quotients in the sense of Gabriel and Bourbaki if the annihilator of any ideal I is equal to zero.Translated from Matematicheskie Zametki, Vol. 7, No. 3, pp. 349–358, March, 1970.I wish to thank L. A. Skornyakov for his help in writing this paper.