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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The structure of semiprimary and Noetherian hereditary rings


Authors: John Fuelberth and James Kuzmanovich
Journal: Trans. Amer. Math. Soc. 212 (1975), 83-111
MSC: Primary 16A46
MathSciNet review: 0376754
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0376754-X
PII: S 0002-9947(1975)0376754-X
Keywords: Semiprimary ring, hereditary ring, semihereditary ring, Noetherian ring, nonsingular ring, regular ring, piecewise domain, Goldie prime ring, maximal quotient ring, classical quotient ring, row-finite matrices, flat module, projective module, uniform characteristic
Article copyright: © Copyright 1975 American Mathematical Society