环上的σ-导子

本文研究了σ－导子的扩张问题，并且在本原环上刻化了s－导子。

ON σ-DERIVATIONS OF RINGS

Let σ be a automorphism of ring R. An additive map d of a subring S of Rinto R is called a σ-derivation if d(xy)=d(x)y+σ(x)d(y) for all x, y∈S. In this note, weprove that an σ-derivation of a semiprime ring R can be extended uniquely to a σ-derivation of Qm , where Qm is the maximal right ring of quotient of R. From thischaracterization, we obtain a result of σ-derivation of primitive ring.