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The near-ring of generalized affine transformations

Published online by Cambridge University Press:  17 April 2009

Shalom Feigelstock
Shalom Feigelstock
Affiliation:
Bar-Ilan University, Ramat-Gan, Israel.
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Abstract

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Blackett and Wolfson studied the near-ring Aff (V) consisting of all affine transformations of a vector space V. This notion is generalized here, and the rear-ring Aff (G) consisting of affine-like maps of a nilpotent group G is introduced. The ideal structure, and the multiplication rule for Aff (G) are determined. Finally a near-ring S is introduced which generalized both Aff (G), and Gonshor's abstract affine near-rings. The ideals of S are determined.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 345 - 349
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Blackett, D.W., “The near-ring of affine transformations”, Proc. Amer. Math. Soc. 7 (1956), 517–519.CrossRefGoogle Scholar
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[4]Wolfson, K.G., “Two-sided ideals of the affine near-rings”, Amer. Math. Monthly, 65 (1958), 29–30.CrossRefGoogle Scholar