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On the structure of an endomorphism near-ring

Published online by Cambridge University Press:  20 January 2009

Gary L. Peterson
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If G is an additive (but not necessarily abelian) group and S is a semigroup of endomorphisms of G, the endomorphism near-ring R of G generated by S consists of all the expressions of the form ɛ1s1+…+ɛnsnwhere ɛi=±1 and si∈S for each i. When functions are written on the right, R forms a distributively generated left near-ring under pointwise addition and composition of functions. A basic reference on near-rings which has a substantial treatment of endomorphism near-rings is [6].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 2 , June 1989 , pp. 223 - 229
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Lyons, C. G. and Meldrum, J. D. P., Characterizing series for faithful D.G. near-rings, Proc. Amer. Math. Soc. 72 (1978), 221–227.Google Scholar
2.Lyons, C. G. and Peterson, G. L., Local endomorphism near-rings, Proc. Edinburgh Math. Soc, to appear.Google Scholar
3.Lyons, C. G. and Scott, S. D., A theorem on compatible N-groups, Proc. Edinburgh Math. Soc., 25 (1982), 27–30.Google Scholar
4.Maxson, C. J., On local near-rings, Math. Z. 106 (1968), 197–205.CrossRefGoogle Scholar
5.Maxson, C. J. and Smith, K. C., Centralizer near-rings determined by local rings, Houston J. Math., 11 (1985), 355–366.Google Scholar
6.Meldrum, J. D. P., Near-rings and their links with groups (Pitman, London, 1985).Google Scholar
7.Rotman, J., The theory of groups (Allyn and Bacon, Boston, 1965).Google Scholar
8.Scott, S. D., Tame near-rings and N-groups, Proc. Edinburgh Math. Soc. 23 (1980), 275–296.CrossRefGoogle Scholar