WU Supeng1,2, ZHAO Bin1*
(1 School of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China;2 Department of Mathematics and statistics, Ankang University, Ankang 725000, Shaanxi, China)
Abstract:
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 pseudo-boolean filters are proposed in MTL-algebras, some characteristic theorems are given.
KeyWords:
residuated lattices; nucleus; involutive filter; extended involutive filter; Glivenko filter; relative pseudo-boolean filter
