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Embedding near-rings into polynomial near-rings

Published online by Cambridge University Press:  20 January 2009

John D. P. Meldrum ,
Günter Pilz  and
Yong-Sian So
John D. P. Meldrum
Affiliation:
Dept. of MathematicsUniv. of EdinburghMayfield rdEdinburgh EH9 3JZ, U.K.
Günter Pilz
Affiliation:
Dept. of MathematicsUniv. of EdinburghMayfield rdEdinburgh EH9 3JZ, U.K.
Yong-Sian So
Affiliation:
Institut für MathematikUniversität LinzA-4040 Linz, Austria
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In this paper we will show that large classes of near-rings are embeddable into (or even isomorphic to) near-rings Gν[x] of polynomials over G in a suitably chosen variety ν of Ω-groups.

For near-rings see [2], for polynomials [1]; for near-rings of polynomials over Ω-groups see [3] [4], [5].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 73 - 79
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

REFERENCES

1.Lausch, H., and Nöbauer, W., Algebra of polynomials (North-Holland, Amsterdam, 1973).Google Scholar
2.Pilz, G., Near-rings, (North-Holland, Amsterdam, 1977).Google Scholar
3.Pilz, G. and So, Y. S., Near-rings of polynomials and polynomial functions, J. Austral. Math. Soc. (Series A) 29 (1980), 61–70.CrossRefGoogle Scholar
4.Pilz, G. and So, Y. S., Near-rings of polynomials over Ω-groups, submitted.Google Scholar
5.Pilz, G. and So, Y. S., Generalized distributively generated near-rings, submitted.Google Scholar