相等代数上态的存在性

The existences of states on equality algebras

为了研究有界相等代数上Bosbach态和Riecan态的存在性.证明了有界相等代数ε上有Bosbach态等价于ker(s)是ε的素奇异滤子;得出对合相等代数上的Bosbach态和Riecan态是一致的;并且给出了有界的相等代数ε有Riecan态当且仅当ε存在一个真的弱奇异滤子F.

The aim of this paper is to investigate the existences of Bosbach states and Riecan states on equality algebras.We prove that an equality algebrasεhas Bosbach states if and only ifεhas a prime fantastic lter ker(s).It is concluded that Bosbach states and Riecan states of equality algebras are consistent.Furthermore,we also obtain thatϵhas Riecan states if and only if a proper lter F satis es(WQY)condition.