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Left orders in strongly regular rings

Published online by Cambridge University Press:  14 November 2011

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

Synopsis

In this paper we characterise left orders in strongly regular rings, both for classical left orders and left orders in the sense of Fountain and Gould [2] where the ring of quotients need not have an identity.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Ánh, P. N. and Márki, L.. Left orders in regular rings with minimum condition for principal one-sided ideals. Math. Proc. Cambridge Philos. Soc. 109 (1991), 323333.CrossRefGoogle Scholar
2Fountain, J. and Gould, V.. Orders in rings without identity. Comm. Algebra 18 (1990), 30853110.CrossRefGoogle Scholar
3Fountain, J. and Gould, V.. Straight left orders in rings. Quart. J. Math. Oxford 43 (1992), 303311.CrossRefGoogle Scholar
4Gonchigdorzh, R.. Regular ring of quotients of reduced rings (in Russian). Algebra i Logika 26 (1987), 150164. Correction, Straight left orders in rings. Quart. J. Math. Oxford 43 (1992), 30331127 (1988), 122.Google Scholar
5Gonchigdorzh, R.. Direct product and sheaf representations of rings and their rings of quotients (D. Sc. Thesis, Budapest, 1989).Google Scholar
6Rowen, L.. Ring Theory, vol. 1 (New York: Academic Press, 1988).Google Scholar
7Stenström, B.. Rings of Quotients, Grundlehren der Math. Wiss. 217 (Berlin: Springer, 1975).CrossRefGoogle Scholar
8Utumi, Y.. On rings of which any one-sided quotient rings are two-sided. Proc. Amer. Math. Soc. 14 (1963), 141147.CrossRefGoogle Scholar