Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 21-27 (2004)

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Primeness in near-rings of continuous functions

G.L. Booth and P.R. Hall

University of Port Elizabeth, Port Elizabeth 6000, South Africa

Abstract: Various types of primeness have been considered for near-rings. One of these is the concept of equiprime, which was defined in 1990 by Booth, Groenewald and Veldsman. We will investigate when the near-ring $N_{0}(G)$ of continuous zero-preserving self maps of a topological group $G$ is equiprime. This is the case when $G$ is either $T_{0}$ and 0-dimensional or $T_{0}$ and arcwise connected. We also give conditions for $N_{0}(G)$ to be strongly prime and strongly equiprime. Finally, we apply these results to sandwich near-rings of continuous functions.

Classification (MSC2000): 16Y30, 22A05

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Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.

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