Endomorphism near-rings.

*(English)*Zbl 0203.33601An endomorphism near ring is a near ring generated additively by all the endomorphisms of a (not necessarily commutative) group. Endomorphism near rings furnish the motivation for the concept of a distributively generated near ring. Although distributively generated near rings have been studied extensively, little is known about the structure of endomorphism near rings. In this paper results are presented which enable one to give the elements of the endomorphism near ring of a group which has a nontrivial idempotent function in its endomorphism near ring. The technique involves a Peirce-type decomposition. The results are used to present a detailed picture of the endomorphism near ring of \(S_3\). The conjecture stated in Section 5 has recently been shown to be false.

Reviewer: J. J. Malone

##### MSC:

16Y30 | Near-rings |

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\textit{J. J. Malone} and \textit{C. G. Lyons}, Proc. Edinb. Math. Soc., II. Ser. 17, 71--78 (1970; Zbl 0203.33601)

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##### References:

[1] | DOI: 10.1093/qmath/18.1.293 · Zbl 0153.35801 · doi:10.1093/qmath/18.1.293 |

[2] | DOI: 10.1112/jlms/s1-33.1.95 · Zbl 0084.26202 · doi:10.1112/jlms/s1-33.1.95 |

[3] | DOI: 10.1007/BF01113852 · Zbl 0131.01604 · doi:10.1007/BF01113852 |

[4] | DOI: 10.1007/BF01195153 · Zbl 0101.27202 · doi:10.1007/BF01195153 |

[5] | DOI: 10.2307/2309918 · Zbl 0084.03402 · doi:10.2307/2309918 |

[6] | DOI: 10.1112/plms/s3-8.1.76 · Zbl 0079.26003 · doi:10.1112/plms/s3-8.1.76 |

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