论文标题
关于同性衍生的概念的评论
Remarks on the notion of homo-derivations
论文作者
论文摘要
本文的目的是研究（不同的）同源性概念。这些是环$ r $的加性映射$ f $，也满足身份\ [f（xy）= f（x）y+xf（y）+f（x）f（x）f（y）\ qquad \ left（x，y \ in r \ rigr）， \]或（在其他概念的情况下）方程系统\ [f（xy）= f（x）f（y）\] \ [f（xy）= f（x）y+xf（y）\ qquad \ lest（x，y \ left（x，y \ y \ in r \ right），我们的主要目标是不得调查上述方程。 f（xy）= h（x）h（y）+xk（y）+k（x）y。 \]获得的结果表明，在相当温和的假设下，即使没有添加性假设，同源性也可以完全表征。
The purpose of this paper is to study the (different) notions of homo-derivations. These are additive mappings $f$ of a ring $R$ that also fulfill the identity \[ f(xy)=f(x)y+xf(y)+f(x)f(y) \qquad \left(x, y\in R\right), \] or (in case of the other notion) the system of equations \[ f(xy)=f(x)f(y)\] \[f(xy)=f(x)y+xf(y) \qquad \left(x, y\in R\right).\] Our primary aim is to investigate the above equations without additivity as well as the following Pexiderized equation \[ f(xy)=h(x)h(y)+xk(y)+k(x)y. \] The obtained results show that under rather mild assumptions homo-derivations can be fully characterized, even without the additivity assumption.
