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Left orders in regular rings with minimum condition for principal one-sided ideals

Published online by Cambridge University Press:  24 October 2008

Pham Ngoc Ánh  and
László Márki
Pham Ngoc Ánh
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, H-1364 Budapest, Pf. 127, Hungary
László Márki
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, H-1364 Budapest, Pf. 127, Hungary
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Extract

Based on ideas from semigroup theory, Fountain and Gould [2, 3, 4] introduced a notion of order in a ring which need not have an identity. In some important cases of rings with identity, e.g. if the larger ring is a semisimple artinian ring, this notion coincides with the classical one. The most important result of Fountain and Gould (see [4]) is a Goldie-like characterization of two-sided orders in a regular ring with minimum condition on principal one-sided ideals. In addition, for the same class of rings, a generalization of the Faith–Utumi theorem has been proved by Gould and Petrich[7]. The methods of these papers seem not to work for one-sided orders.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 2 , March 1991 , pp. 323 - 333
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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