关于可加保幂零映射的一点注记

摘要

给出Mn(F) (n2, F=R或C)上所有保幂零可加满射的刻画. 作为应用,得到Mn(C)上保相似性可加满射,保谱等性可加满射以及保特征值相等可加满射的刻画.%All additive surjective maps preserving nilpotency in both directions on Mn(F) (n2, F=R or C) are characterized. As applications, the additive surjections on Mn(C) which preserve respectively the similarity, the relation of spectrum equality and the relation of eigenvalue equality are classified.