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Essential ideals of incidence algebras

Published online by Cambridge University Press:  09 April 2009

Eugene Spiegel
Affiliation:
Department of Mathematics University of Connecticut Storrs, CT 06269 USA e-mail: spiegel@math.uconn.edu
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Abstract

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It is determined when there exists a minimal essential ideal, or minimal essential left ideal, in the incidence algebra of a locally finite partially ordered set defined over a commutative ring. When such an ideal exists, it is described.

MSC classification

Secondary: 16D25: Ideals
Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Doubilet, P., Rota, G.-C. and Stanley, R. P., ‘On the foundation of combinatorial theory VI: The idea of generating function’, in: Finite operator calculus (Academic Press, New York, 1975) pp. 267318.Google Scholar
[2]Green, B. W. and Van Wyk, L., ‘On the small and essential ideals in certain classes of rings’, J. Austral. Math. Soc. (Series A) 46 (1989), 262271.CrossRefGoogle Scholar
[3]Loi, N. V. and Wiegandt, R., ‘Small ideals and the Brown-McCoy radical’, Radical theory (Eger 1982), Colloq. Math. Soc. János Bolyai 38 (North Holland, Amsterdam, 1985).Google Scholar
[4]Rowen, L., Ring theory, vol. I (Academic Press, Boston, 1988).Google Scholar
[5]Spiegel, E. and O'Donnell, C. J., Incidence algebras (Marcel Dekker, New York, 1977).Google Scholar