The structure of semiprimary and Noetherian hereditary rings

Fuelberth, John; Kuzmanovich, James

doi:10.1090/S0002-9947-1975-0376754-X

The structure of semiprimary and Noetherian hereditary rings
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by John Fuelberth and James Kuzmanovich PDF

Trans. Amer. Math. Soc. 212 (1975), 83-111 Request permission

Abstract:

In the first portion of this paper a structure theorem for semiprimary hereditary rings is given in terms of $M \times M$ “triangular” row-finite matrices over a division ring D. This structure theorem differs from previous theorems of this type in that the representation is explicit in terms of matrices over a division ring. In the second portion of this paper we are able to apply the results of Gordon and Small to obtain a structure theorem for semihereditary and left hereditary rings which are left orders in a semiprimary ring. In the case of the left hereditary rings, the representation is explicit in terms of matrices over left hereditary Goldie prime rings and their respective classical left quotient rings. As an application we obtain, by a different method, a non-Noetherian generalization of a result of Chatters which states that a two-sided hereditary Noetherian ring is a ring direct sum of an Artinian ring and a semiprime ring.

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