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One-sided ideals in near-rings of transformations

Published online by Cambridge University Press:  09 April 2009

H. E. Heatherly
H. E. Heatherly
Affiliation:
University of Southwestern LouisianaLafayette, Louisiana
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Let (G, +) be an arbitrary group and let T0(G) = {f∈ Map(G, G): 0f = 0}; the system composed of T0(G) and the operations of pointwise addition and composition of functions form a (left) near-ring. Berman and Silverman, in their investigation of near-rings of transformations [3], found that for every group G the associated near-ring of transformations T0(G) has no proper ideals. In the present paper left and right ideals of T0(G) are considered.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 2 , March 1972 , pp. 171 - 179
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Beidleman, J. C., On near-rings and near-ring modules (Doctoral Dissertation, Pennsylvania State University, 1964).Google Scholar
[2]Beidleman, J. C., ‘A radical for near-ring modules’, Michigan Math. J., 12 (1965), 377–383.CrossRefGoogle Scholar
[3]Berman, G. and Silverman, R. J., ‘Simplicity of near-rings of transformations’, Proc. Amer. Math. Soc., 10 (1959), 456–459.CrossRefGoogle Scholar
[4]Blackett, D. W., Simple and semi-simple near-rings (Doctoral Dissertation, Princeton University, 1950).Google Scholar
[5]Malone, J. J. Jr and Heatherly, H. E., ‘Some near-ring embeddings’, Quart. J. Math. Oxford (2), 20 (1969), 81–85.CrossRefGoogle Scholar