Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T21:25:18.295Z Has data issue: false hasContentIssue false

Matrix d.g. near-rings

Published online by Cambridge University Press:  20 January 2009

Rights & Permissions [Opens in a new window]

Abstract

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.

Matrix near-rings had been defined by Meldrum and Van der Walt in 1986 and although a fair amount of results on the structure of these near-rings have been obtained since then, a satisfactory structure theory has yet to be developed for matrix d.g. near-rings. In this paper we give an alternate definition (in fact the dual definition) for matrix d.g. near-rings and develop a satisfactory structure theory for such d.g. near-rings.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1. Abbasi, S. J., Distributively generated matrix near-rings, Preprint 93/79, International Centre for Theoretical Physics, Trieste, Italy, 1993.Google Scholar
2. Abbasi, S. J. and Meldrum, J. D. P., On matrix near-rings, Math. Pannon. 2 (1991), 107113.Google Scholar
3. Abbasi, S. J., Meldrum, J. D. P. and Meyer, J. H., The J o-radical of matrix near-rings, Arch. Math. 56 (1991), 137139.CrossRefGoogle Scholar
4. Beidleman, J. C., On near-rings and near-ring modules (Doctoral dissertation, Pennsylvania State University, 1964).Google Scholar
5. Fröhlich, A., Distributively generated near-rings (I, Ideal Theory), Proc. London Math. Soc. (3) 8 (1958), 7694.CrossRefGoogle Scholar
6. Fröhlich, A., Distributively generated near-rings (II. Representation Theory), Proc. London Math. Soc. (3) 8 (1958), 95108.Google Scholar
7. Fröhlich, A., On groups over a d.g. near-ring I, Quart. J. Math. Oxford Ser. (2) 11 (1960), 193210.CrossRefGoogle Scholar
8. Fröhlich, A., On groups over a d.g. near-ring II, Quart. J. Math. Oxford Ser. (2) 11 (1960), 211228.CrossRefGoogle Scholar
9. Heatherly, H. E., Matrix near-rings, J. London Math. Soc. (2) 7 (1973), 355356.CrossRefGoogle Scholar
10. Ligh, S., A note on matrix near-rings, J. London Math. Soc. (2) 11 (1975), 383384.CrossRefGoogle Scholar
11. Meldrum, J. D. P., Near-rings and their links with groups (Research Notes in Mathematics, Pitman, 134, 1985).Google Scholar
12. Meldrum, J. D. P., Matrix near-rings, Contrib. Gen. Alg. 8 (ed. Pilz, G., Holder-Pichler-Tempsky, Wien 1992, 189204).Google Scholar
13. Meldrum, J. D. P. and Meyer, J. H., Intermediate ideals in matrix near-rings, Paper presented to the International Conference in Near-rings and Near-fields held at Hamburg in August, 1995.Google Scholar
14. Meldrum, J. D. P. and Van der Walt, A. P. J., Matrix near-rings, Arch. Math. 47 (1986), 312319.CrossRefGoogle Scholar
15. Meyer, J. H., Matrix near-rings (Ph.D. thesis, Stellenbosch University, South Africa, 1986).Google Scholar
16. Neumann, Hanna, On varieties of groups and their associated near-rings, Math. Z. 65 (1956), 3669.CrossRefGoogle Scholar
17. Tharmaratinam, V., Complete primitive distributively generated near-rings, Quart. J. Math. Oxford Ser. (2) 18 (1967), 293313.CrossRefGoogle Scholar
18. Tharmaratinam, V., Endomorphism near-ring of a relatively free group, Math. Z. 113 (1970), 119135.CrossRefGoogle Scholar
19. Tharmaratinam, V., Division d.g. near-rings, J. London Math. Soc. (2) 14 (1976), 135147.CrossRefGoogle Scholar
20. Tharmaratinam, V., Division d.g. near-rings II, Bull. Austral. Math. Soc. 35 (1987), 7380.CrossRefGoogle Scholar
21. Tharmaratinam, V., Regular topological distributively generated near-rings, Bull. Austral. Math. Soc. 35 (1987), 5972.CrossRefGoogle Scholar
22. Van der Walt, A. P. J., Primitivity in matrix near-rings, Quaestiones Math. 9 (1986), 459469.CrossRefGoogle Scholar
23. Van der Walt, A. P. J., On two sided ideals in matrix near-rings, in Near-rings and Near-fields (ed. Betsch, G., North Holland, Amsterdam, 1987), 267272.Google Scholar