Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T22:34:07.270Z Has data issue: false hasContentIssue false
  • English
  • Français

The representation of d. g. near-rings

Published online by Cambridge University Press:  09 April 2009

J. D. P. Meldrum
J. D. P. Meldrum
Affiliation:
Mathematical Institute University of EdinburghEdinburgh, Scotland.
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.

In this paper we study the problem of the representation of d.g. near-rings, and in particular the problem of a faithful representation, which is equivalent to the adjoining of an identity. This problem has been considered by Malone [5] and Malone and Heatherly [6] and [7]. They have shown that a finite near-ring with two sided zero can be embedded in the d.g. near-ring generated by the inner automorphisms of a suitable group, and that an identity can always be adjoined to a near-ring with two sided zero. They have also given some special conditions under which a faithful representation of a d.g. near-ring exists.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 467 - 480
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Fröhlich, A., ‘Distributively generated near-rings (I): Ideal theory’, Proc. London Math. Soc. (3) 8 (1958), 74–94.Google Scholar
[2]Fröhlich, A., ‘Distributively generated near-rings (II): Representation theory’, Proc. London Math. Soc. (3) 8 (1958), 95–108.Google Scholar
[3]Fröhlich, A., ‘On groups over a d.g. near-ring (I): Sum constructions and free R-groups’, Quart. J. Math. (Oxford) (2) 11 (1960), 193–210.CrossRefGoogle Scholar
[4]Fröhlich, A., ‘On groups over a d.g. near-ring (II): Categories and Functors’, Quart. J. Math. (Oxford) (2) 11 (1960), 211–228.CrossRefGoogle Scholar
[5]Malone, J. J., ‘A near ring analogue of a ring embedding theorem’, J. Algebra 16 (1970), 237–238.CrossRefGoogle Scholar
[6]Malone, J. J. and Heatherly, H. E., ‘Some near-ring embeddings’, Quart. J. Math. (Oxford) (2) 20 (1969), 81–85.CrossRefGoogle Scholar
[7]Malone, J. J. and Heatherly, H. E., ‘Some near-ring embeddings (II)’, Quart. J. Math. (Oxford) (2) 21 (1970), 445–448.Google Scholar
[8]Neumann, Hanna, Varieties of Groups (Springer, Berlin, 1967).CrossRefGoogle Scholar