Malone, J. J.; Lyons, C. G. Endomorphism near-rings. (English) Zbl 0203.33601 Proc. Edinb. Math. Soc., II. Ser. 17, 71-78 (1970). An 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 17 Documents MSC: 16Y30 Near-rings Keywords:endomorphism near ring; nontrivial idempotent function; Peirce-type decomposition PDFBibTeX XMLCite \textit{J. J. Malone} and \textit{C. G. Lyons}, Proc. Edinb. Math. Soc., II. Ser. 17, 71--78 (1970; Zbl 0203.33601) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.