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The 2-primitive ideals of structural matrix near-rings

Published online by Cambridge University Press:  20 January 2009

L. Van Wyk
L. Van Wyk
Affiliation:
Department of MathematicsUniversity of StellenboschStellenbosch 7600South Africa
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An isomorphism (as groups) is established between an arbitrary connected module over a structural matrix near-ring and a direct sum of appropriate modules over the base near-ring. This isomorphism leads to a characterization of the 2-primitive ideals of a structural matrix near-ring.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 229 - 239
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Heatherly, H. E., Matrix near-rings, J. London Math. Soc. (2) 7 (1973), 355–356.CrossRefGoogle Scholar
2.Meldrum, J. D. P., Near-Rings and their Links with Groups (Research Notes in Mathematics 134, Pitman, London, 1985).Google Scholar
3.Meldrum, J. D. P. and Van Der Walt, A. P. J., Matrix near-rings, Arch. Math. 47 (1986), 312–319.CrossRefGoogle Scholar
4.Meyer, J. H., Left ideals in matrix near-rings, Comm. Algebra 17 (1989), 1315–1335.CrossRefGoogle Scholar
5.Meyer, J. H., Matrix near-rings (Doctoral Dissertation, University of Stellenbosch, South Africa, 1986).Google Scholar
6.Meyer, J. H. and Van Der Walt, A. P. J., Solution of an open problem concerning 2-primitive near-rings, in Near-Rings and Near-Fields (G. Betsch, editor, Elsevier Science Publishers B.V., North-Holland, Amsterdam, 1987).Google Scholar
7.Pilz, G., Near-Rings (Revised edition, North-Holland, Amsterdam, 1983).Google Scholar
8.Van Der Walt, A. P. J., Matrix representation of 2-primitive near-rings with minimal subgroups, preprint.Google Scholar
9.Van Der Walt, A. P. J., On two-sided ideals in matrix near-rings, in Near-Rings and Near-Fields (G. Betsch, editor, Elsevier Science Publishers B.V., North-Holland, Amsterdam, 1987.)Google Scholar
10.Van Der Walt, A. P. J., Primitivity in matrix near-rings, Quaestiones Math. 9 (1986), 459–469.CrossRefGoogle Scholar
11.Van Der Walt, A. P. J. and Van Wyk, L., The J2-radical in structural matrix near-rings, J. Algebra 123 (1989), 248–261.CrossRefGoogle Scholar
12.Van Wyk, L., Special radicals in structural matrix rings, Comm. Algebra 16 (1988), 421–435.CrossRefGoogle Scholar
13.Wauters, P. and Jespers, E., Rings graded by an inverse semigroup with finitely many idempotents, preprint.Google Scholar