A generalized ring homomorphisms equation

被引：18

作者：

Ger, Roman ^{[2
]}

Reich, Ludwig ^{[1
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Wissenschaftliches Rechnen, A-8010 Graz, Austria

[2] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

来源：

MONATSHEFTE FUR MATHEMATIK | 2010年 / 159卷 / 03期

关键词：

Ring homomorphism; Additivity and multiplicativity; Functional equations of Dhombres and Alzer; General solution;

D O I：

10.1007/s00605-009-0173-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deal with the functional equation af (xy) + bf (x) f (y) + cf (x + y) + df (x) + kf (y) = 0 (*) yielding a joint generalization of equations that has been studied by Dhombres (Aequationes Math 35: 186-212, 1988), H. Alzer (private communication) and Ger (Publ Math Debrecen 52: 397-417, 1998; Rocznik Nauk-Dydakt Prace Mat 17: 101115, 2000). We are looking for solutions f of equation (*) mapping a given unitary ring into an integral domain. We continue Dhombres' studies with the emphasis given upon the dropping of the 2-divisibility assumption in the domain. Among others, our aim is to find suitable conditions under which a function f satisfying (*) yields a homomorphism between the rings in question.

引用

页码：225 / 233

页数：9