Vol. 51, No. 2, 1974

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On finite left localizations

Robert S. Cunningham

Vol. 51 (1974), No. 2, 407–415

Of the several types of noncommutative quotient rings, finite left localizations have structure most like that of the original ring. This paper examines finite left localizations from two points of view: As rings of quotients with respect to hereditary torsion classes, and as endomorphism rings of finitely generated projective modules. In the first case, finite left localizations are shown to be the rings of quotients with respect to perfect TTF-classes. In the second, they are shown to be the double centralizers of finite projectors.

Mathematical Subject Classification
Primary: 16A08
Received: 8 January 1973
Published: 1 April 1974
Robert S. Cunningham