非交换剩余格上的n重PMTL滤子及其刻画

n-fold PMTL-filters and Their Characterizations in Non-Commutative Residuated Lattices

滤子理论在多值逻辑及其相关代数的研究中起到非常重要的作用.在非交换剩余格上引入n重PMTL滤子的概念,给出这类滤子的一系列刻画.提出n重PMTL代数的定义,从n重PMTL滤子的角度证明n重PMTL代数的若干特征定理,并引入n重素滤子的概念,得到n重PMTL代数的另一种刻画.

The filter theory plays an important role in studying multiple-valued logic and the related algebras. This paper introduces the concept of the n -fold PMTL-filters in non-commutative residuated lattices. Several characterizations of n -fold PMTL- filters are derived. The concept of n -fold PMTL-algebra is proposed, and several characteristic theorems of n -fold PMTL-algebra are proved from the perspective of n -fold PMTL-filters. Finally, the concept of n -fold prime filter is introduced to obtain another description of n -fold PMTL-algebra.