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Near-rings of polynomials and polynomial functions

Part of: Algebraic structures

Published online by Cambridge University Press:  09 April 2009

Günter Pilz  and
Yong-Sian so
Günter Pilz
Affiliation:
Institut für Mathematik, Universität LinzA-4045 Linz, Austria
Yong-Sian so
Affiliation:
Institut für Mathematik, Universität LinzA-4045 Linz, Austria
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Abstract

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In this paper we investigate near-rings of polynomials and polynomial functions. After some results which belong to universal algebra we turn our attention to the familiar case of polynomials and polynomial functions over a commutative ring with identity. We study the relation between ring- and near-ring homomorphisms, and the behaviour of polynomial near-rings when the ring splits into a direct sum. A discussion of the structure of these polynomial near-rings (radical, semisimplicity) finishes this paper. These investigations are motivated by Clay and Doi (1973).

MSC classification

Secondary: 08A40: Operations, polynomials, primal algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 61 - 70
Copyright
Copyright © Australian Mathematical Society 1980

References

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