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Near-rings of polynomials over groups

Published online by Cambridge University Press:  20 January 2009

J. D. P. Meldrum ,
G. Pilz  and
Y. S. So
J. D. P. Meldrum
Affiliation:
Department of MathematicsUniversity of EdinburghMayfield Road, Edinburgh EH9 3JZ, Scotland
G. Pilz
Affiliation:
Institutut Für Mathematik Johannes Kepler UniversitätA-4040 Linz, Austria
Y. S. So
Affiliation:
Department of Mathematics, Tunghai University Taichung, Taiwan 400, Republic of China
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The set G[x] of polynomials over a group (G, + )—as well as the polynomial functions P(G) on (G, +) form near-rings with respect to addition and composition (substitution). See [1] for polynomials and [2] for near-rings. A number of results on G[x] can be deduced from [2].

Due to [1], the polynomials in G[x] can uniquely be represented in the following “normal form”:

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 1 - 7
Copyright
Copyright © Edinburgh Mathematical Society 1985

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 over Ω-groups, Monatsh. Math. 91 (1981), 73–76.CrossRefGoogle Scholar
4.Meldrum, J. D. P., Pilz, G. and So, Y. S., Embedding near-rings into polynomial near-rings, Proc. Edinburgh Math. Soc. 25 (1982), 73–79.CrossRefGoogle Scholar