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Positive derivations on partially ordered strongly regular rings

Part of: Ordered structures

Published online by Cambridge University Press:  09 April 2009

D. J. Hansen
D. J. Hansen
Affiliation:
Department of Mathematics North Carolina State UniversityRaleigh, North Carolina 27650, U.S.A.
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Abstract

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The author presents a proof that a partially ordered strongly regular ring S which has the additional property that the square of each member of S is greater than or equal to zero cannot have nontrivial positive derivations.

Keywords

positive derivationstrongly regular ringp. o. ring.

MSC classification

Secondary: 06F25: Ordered rings, algebras, modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 178 - 180
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Colville, P., Davis, G., and Keimel, K., ‘Positive derivations on f-rings’, J. Austral. Math. Soc. Ser. A 23 (1977), 371–375.CrossRefGoogle Scholar
[2]Dai, Taen-yu and Demarr, R., ‘Positive derivations on partially ordered linear algebras with an order unit’, Proc. Amer. Math. Soc. 72 (1978), 21–26.CrossRefGoogle Scholar
[3]Fuchs, L., Partially ordered algebraic systems (Pergamon Press, 1963).Google Scholar