关联代数上Jordan τ-中心化子

Jordan τ-centralizers on incidence Algebras

设(X,≤)是一个有限预序集,R是含单位元的交换环.I(X,R)是在R上定义关于X的关联代数,证明了关联代数上的左Jordan中心化子是左中心化子以及关联代数上的左Jordan τ-中心化子是左τ-中心化子,进一步证明了关联代数上的Jordan中心化子是中心化子以及关联代数上的Jordan τ-中心化子是τ-中心化子.

Let(X,≤)be a finite pre-ordered set,R a commutative ring with the identity.I(X,R)the incidence algebra of X over R.It is proved that the left Jordan centralizer on the incidence algebra is left centralizers and the left Jordan τ-centralizers on the incidence algebra is left τ-centralizers,moreover proved that the Jordan centralizer on the incidence algebra is centralizers and the Jordan τ-centralizers on the incidence algebra is τ-centralizers.