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The near-ring of generalized affine transformations

  • Shalom Feigelstock (a1)

Abstract

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.

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Copyright

References

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[1]Blackett, D.W., “The near-ring of affine transformations”, Proc. Amer. Math. Soc. 7 (1956), 517519.
[2]Gonshor, H., “On abstract affine near-rings”, Pac. J. Math. 14 (1964), 12371240.
[3]Pilz, G., Near-rings, (North Holland, New York, 1977).
[4]Wolfson, K.G., “Two-sided ideals of the affine near-rings”, Amer. Math. Monthly, 65 (1958), 2930.
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The near-ring of generalized affine transformations

  • Shalom Feigelstock (a1)

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