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Endomorphisms and Distributive Elements in Near-Rings Determined by Rings and Modules

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Abstract

For a unitary, faithful R-module V, the centralizer near-ring determined by R and V, denoted by MR(V), contains, as a sub-ring, the set of distributive elements of MR(V), denoted by Dist(MR(V)). The ring Dist(MR(V)) always contains the ring EndR(V). In this paper we discuss conditions which force EndR(V) = Dist(MR(V)) as well as conditions which force MR(V) = Dist(MR(V)).

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Authors and Affiliations

  1. 2300 Broadmoor Apt. 7, Bryan, TX, 77802

    Andrew M. Diener

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  1. Andrew M. Diener
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Correspondence to Andrew M. Diener.

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This paper was written as a part of my dissertation under the direction of Dr. C. J. Maxson

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Diener, A.M. Endomorphisms and Distributive Elements in Near-Rings Determined by Rings and Modules. Results. Math. 38, 226–234 (2000). https://doi.org/10.1007/BF03322010

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  • DOI: https://doi.org/10.1007/BF03322010

2000 Mathematics subject classification (Amer. Math. Soc.)

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