剩余格中基于核映射的滤子

The filters based on nuclei in residuated lattices

在剩余格中,基于核映射引入了对合滤子、扩展对合滤子、Glivenko滤子的概念,讨论了它们的性质且给出了它们的特征定理。分析了滤子的一种带有核映射的扩张形式的代数性质,得到了扩展对合滤子的应用。进一步,在MTL代数中引入了相对伪布尔滤子的概念,得到了相对伪布尔滤子的特征定理。

The notions of the extended involutive and Glivenko filters based on nuclei in residuated lattices are defined and some properties of them are discussed,their characteristic theorems are obtained.Based on nuclei,algebraic properties of the extended set of the filter are introduced and then an application of extended involutive filters is showed.The concepts of relative pseudoboolean filters are proposed in MTL-algebras,some characteristic theorems are given.