Vol. 80, No. 2, 1979

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On the structure of finitely generated splitting rings

John Fuelberth and James J. Kuzmanovich

Vol. 80 (1979), No. 2, 389–424
Abstract

In this paper the structure of finitely generated splitting rings for the Goldie theory is studied. First, right nonsingular finitely generated splitting rings with essential socle which either are right finite dimensional or are right orders in a semiprimary ring are characterized. This characterization is in terms of an explicit triangular matrix structure for R. Then right nonsingular finitely generated splitting rings with zero socle are shown to be right finite dimensional if and only if they are right orders in a semiprimary ring. An explicit triangular structure is given for this class of rings as well. For certain classes of right nonsingular right finite dimensional finitely generated splitting rings with zero socle, the structure theorem can be simplified somewhat. Then right nonsingular right finite dimensional finitely generated splitting rings are characterized as a certain essential product of a ring with essential socle and one with zero socle. Right nonsingular finitely generated splitting rings which are right orders in a semiprimary ring are shown to be a direct product of a ring with essential socle and a ring with zero socle. Finally, some comments are made showing how some of these results can be applied to bounded splitting rings and splitting rings.

Mathematical Subject Classification
Primary: 16A08, 16A08
Secondary: 16A63, 16A12
Milestones
Received: 15 June 1977
Revised: 29 March 1978
Published: 1 February 1979
Authors
John Fuelberth
James J. Kuzmanovich