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The J0-Radical of a Matrix Nearring can be Intermediate

Published online by Cambridge University Press:  20 November 2018

J. D. P. Meldrum
Affiliation:
Department of Mathematics & Statistics University of Edinburgh James Clerk Maxwell Building The King’s Buildings Mayfield Road Edinburgh EH9 3JZ United Kingdom, e-mail: [email protected]
J. H. Meyer
Affiliation:
Department of Mathematics University of the Orange Free State PO Box 339 9300 Bloemfontein Republic of South Africa, e-mail: [email protected]
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Abstract

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An example is constructed to show that the J0-radical of a matrix nearring can be an intermediate ideal. This solves a conjecture put forward in [1].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Meldrum, J. D. P. and Meyer, J. H., Intermediate ideals in matrix near-rings, Comm. Alg. (5)24 (1996), 16011619.Google Scholar
2. Meldrum, J. D. P. and Meyer, J. H., Modules over matrix near-rings and the J0-radical, Monatsh. Math. 112 (1991), 125139.Google Scholar
3. Meldrum, J. D. P. and van der Walt, A. P. J., Matrix near-rings, Arch.Math. 47 (1986), 312319.Google Scholar
4. Meyer, J. H., Chains of intermediate ideals in matrix near-rings, Arch.Math. 63 (1994), 311315.Google Scholar
5. Meyer, J. H., Left ideals and 0-primitivity in matrix near-rings, Proc. Edinburgh Math. Soc. 35 (1992), 173187.Google Scholar
6. van der Walt, A. P. J., On two-sided ideals in matrix near-rings, In: Near-rings and Near-fields, (ed. G. Betsch), North-Holland, 1987, 267–272.Google Scholar
7. van der Walt, A. P. J., Primitivity in matrix near-rings, Quaestiones Math. 9 (1986), 459469.Google Scholar