剩余格上Riean态的存在性

On the Existence of Riean States on Residuated Lattices

在good剩余格上研究Riean态的存在性。证明了good剩余格上Riean态的核是一个真弱正规滤子,但不是正规滤子。进一步,给出了good剩余格上Riean态存在的充分必要条件。此外,证明了可表示剩余格至多只有一个固定点。

The aim of this paper is to study the existence of Riecan states on good residuated lattices.We prove that the kernel of Riecan states on good residuated lattices is a proper weak normal filter,and is not a normal filter.Furthmore,the necessary and sufficient conditions for good residuated lattices having Riecan states are obtained.In addition,the fixpoint of residuated lattices is investigated and it is proved that each representable residuated lattice has at most one fixpoint.