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On the structure of morphism near-rings*

Published online by Cambridge University Press:  14 November 2011

J. D. P. Meldrum
J. D. P. Meldrum
Affiliation:
Department of Mathematics, University of Edinburgh
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Synopsis

The connection between the structure of a near-ring and that of the group on which it acts is used to obtain results concerning the structure of near-rings. A generalized R series is defined for an R module, where R is a zero-symmetric left near-ring, and it is shown that all R modules have maximal R series. The idea of a near-ring which annihilates a series is introduced and some easy consequences of the definition are pointed out. Semi-primitive near-rings are introduced and a general structural result connecting the last two ideas is given. Some special cases which generalize earlier results on endomorphism near-rings are stated. Finally some of the limitations of the idea of semi-primitive near-rings are shown, and some applications are given, in particular to the endomorphism near-rings of soluble groups and of the symmetric groups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 3-4 , 1978 , pp. 287 - 298
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Betsch, G.Primitive Near-rings. Math. Z. 130 (1973), 351–361.CrossRefGoogle Scholar
2Fröhlich, A.Distributively generated near-rings (I) Ideal theory. Proc. London Math. Soc. 8 (1958), 74–94.Google Scholar
3Fröhlich, A.The near-ring generated by the inner automorphisms of a finite simple group. J. London Math. Soc. 33 (1958), 95–107.Google Scholar
4Hall, P. and Hartley, B.The stability group of a series of subgroups. Proc. London Math. Soc. 16 (1966), 1–39.CrossRefGoogle Scholar
5Johnson, M. J.Radicals of endomorphism near rings. Rocky Mountain J. Math. 3 (1973), 1–7.CrossRefGoogle Scholar
6Laxton, R. R.Primitive distributively generated near-rings. Mathematika 8 (1961), 142–158.CrossRefGoogle Scholar
7Lyons, C. G. and Meldrum, J. D. P.Characterizing series for faithful d.g. near-rings. Proc. Amer. Math. Soc., in press.Google Scholar
8Malone, J. J. and Heatherly, H. E.Some near-ring embeddings. Quart. J. Math. Oxford Ser. 20 (1969), 81–85.CrossRefGoogle Scholar
9Meldrum, J. D. P.The representation of d.g. near-rings. J. Austral. Math. Soc. 16 (1973), 467–480.CrossRefGoogle Scholar
10Robinson, D. J. S.Finiteness conditions and generalised soluble groups (Berlin: Springer, 1972).Google Scholar
11Scott, W. R.Group Theory. (Englewood Cliffs. N.J.: Prentice-Hall. 1964).Google Scholar