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Distributive elements in the near-rings of polynomials

Published online by Cambridge University Press:  20 January 2009

Jaime Gutierrez  and
Carlos Ruiz De Velasco Y Bellas
Jaime Gutierrez
Affiliation:
Departmento de MatematicasFacultad de CienciasUniversidad de Cantabria39005-Santander, Spain.
Carlos Ruiz De Velasco Y Bellas
Affiliation:
Departmento de MatematicasFacultad de CienciasUniversidad de Cantabria39005-Santander, Spain.
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As usual in the theory of polynomial near-rings, we deal with right near-rings. If N = (N, +,·) is a near-ring, the set of distributive elements of N will be denoted by Nd;

It is easy to check that, if N is an abelian near-ring (i.e., r + s = s + r, for all r, s∈N), then Nd is a subring of N.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 73 - 80
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Lausch, H. and Nöbauer, W., Algebra of polynomials, (North-Holland, Amsterdam-New York, 1973).Google Scholar
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3.Ore, O., On a special class of polynomials, Trans. Amer. Math. Soc. 35 (1933), 539–584.Google Scholar
4.Pilz, G., Near-rings (North-Holland, Amsterdam, 1983).Google Scholar