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Homogeneous Maps of Free Ring Modules

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 336))

Abstract

Given an R-module V, the near-ring of homogeneous maps M R(V) is the set of maps for all rR and vV under point-wise addition and composition of functions. When R is an integral domain and V is a finitely generated free module, the set will be described for any fixed element v in V.

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References

  1. R. Gilmer, Multiplicative ideal theory. Marcel Dekker, Inc., Pure and Applied Mathematics, vol. 12, New York, 1972.

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  2. W. Heinzer, Integral domains in which each non-zero ideal is divisorial, Mathematica 15 (1968), 164–170.

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  3. C. J. Maxson and A. P. J. van der Walt, Homogeneous maps as piecewise endomorphisms, Comm. in Alg. 20 (1992), 2755–2776.

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  4. J. D. P. Meldrum, Near-rings and their links with groups, Pitman Research Notes Series, No. 134, 1985.

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© 1995 Springer Science+Business Media Dordrecht

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van der Merwe, A.B. (1995). Homogeneous Maps of Free Ring Modules. In: Fong, Y., Bell, H.E., Ke, WF., Mason, G., Pilz, G. (eds) Near-Rings and Near-Fields. Mathematics and Its Applications, vol 336. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0359-6_28

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  • DOI: https://doi.org/10.1007/978-94-011-0359-6_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4160-7

  • Online ISBN: 978-94-011-0359-6

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