Normal filters in residuated lattices

  • Lida Torkzadeh Islamic azad universiyty of Kerman
  • A. Ahadpanah Department of Mathematics, Science and Research Branch, Islamic Azad University, Kerman, Iran
Keywords: Residuated lattice, (normal, prime, Boolean, fantastic, implicative, positive implicative, obstinate, involution) filter, MV-filter, G-filter


Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice.