Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T12:39:01.441Z Has data issue: false hasContentIssue false
  • English
  • Français

Endomorphism near-rings

Published online by Cambridge University Press:  20 January 2009

J. J. Malone  and
C. G. Lyons
C. G. Lyons
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The study of near-rings is motivated by consideration of the system generated by the endomorphisms of a (not necessarily commutative) group. Such endomorphism near-rings also furnish the motivation for the concept of a distributively generated (d.g.) near-ring. Although d.g. near-rings have been extensively studied, 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 given group. Also, some results relating to the right ideal structure of an endomorphism near-ring are presented. These concepts are applied to present a detailed picture of the properties of the endomorphism near-ring of (S3, +).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 71 - 78
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Beidleman, J. C., Distributively generated near-rings with descending chain condition, Math. Z. 91 (1966), 65–69.CrossRefGoogle Scholar
(2) Berman, G. and Silverman, R. J., Near-rings, Amer. Math. Monthly 66 (1959), 23–34.CrossRefGoogle Scholar
(3) Betsch, G., Ein Radikal für Fastringe, Math. Z. 78 (1962), 86–90.CrossRefGoogle Scholar
(4) Chandy, A. J., Rings generated by inner automorphisms of non-abelian groups, Doctoral Dissertation, Boston University, 1965.Google Scholar
(5) Fröhlich, A., Distributively generated near-rings, Proc. London Math. Soc.(3) 8 (1958), 76–108.CrossRefGoogle Scholar
(6) Fröhlich, A., The near-ring generated by the inner automorphisms of a finite simple group, J. London Math. Soc. 33 (1958), 95–107.Google Scholar
(7) Heatherly, H. E., Embedding of near-rings, Doctoral Dissertation, Texas A&M University, 1968.Google Scholar
(8) Tharmaratnam, V., Complete primitive distributively generated near-rings, Quart. J. Math. Oxford Ser. (2) 18 (1967), 293–313.CrossRefGoogle Scholar