Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - February 1985 - Volume 28, Issue 01  

Research Article

Near-rings of polynomials over groups

J. D. P. Meldruma1, G. Pilza2 and Y. S. Soa3

a1 Department of Mathematics University of Edinburgh Mayfield Road, Edinburgh EH9 3JZ, Scotland

a2 Institutut Für Mathematik Johannes Kepler Universität A-4040 Linz, Austria

a3 Department of Mathematics, Tunghai University Taichung, Taiwan 400, Republic of China

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”:

S001309150000314X_eqn1

(Received November 09 1983)