Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-11T08:25:36.623Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Clay, J. R. and Doi, D. K. (1973), ‘Maximal ideals in the near-ring of polynomials over a field’, Colloq. Math. Soc. János Bolyai 6, (Keszthely (Hungary), North-Holland, 1973), 117–133.Google Scholar
Keller, G. and Olson, F. R. (1968), ‘Counting polynomial functions (mod pn)’, Duke Math. J. 35, 835–838.Google Scholar
Kempner, A. J. (1921), ‘Polynomials and their residue systems’, Trans. Amer. Math. Soc. 22, 240–288.CrossRefGoogle Scholar
Lausch, H. and Nöbauer, W. (1973), Algebra of polynomials (North-Holland, Amsterdam-New York).Google Scholar
Müller, W. and Eigenthaler, G. (1979), ‘A remark on polynomial functions over finite commutative rings with identity’, Boletin da Sociedade Brasileira da Matemática (to appear).CrossRefGoogle Scholar
Nöbauer, W. (1974), ‘Compatible and conservative functions on residue-class rings of the integers’, Colloq. Math. Soc. János Bolyai 13 (Debrecen (Hungary)), 245–257.Google Scholar
Nöbauer, W. (1976), ‘Üeber die affin vollständigen, endlich erzeugbaren Moduin’, Monatsh. Math. 82, 187–198.CrossRefGoogle Scholar
Pilz, G. (1977), Near-rings (North-Holland, Amsterdam-New York).Google Scholar
So, Y. S. (1977), Polynom-Fastringe (Dissertation, Universität, Linz (Austria), and Institutsbericht Nr., 85, Institut für Mathematik, Universität Linz).Google Scholar
Straus, E. G. (1974), ‘Remarks on the paper “Ideals in near-rings of polynomials over a field”’, Pacific J. Math. 52, 601–603.CrossRefGoogle Scholar
Werner, H. (1971), ‘Produkte von Kongruenzklassengeometrien universeller Algebren’, Math. Z. 121, 111–140.CrossRefGoogle Scholar