A new approach for classification of filters in residuated lattices

In the mathematical literature, many types of filters in residuated lattices or in special classes of residuated lattices (BL-algebras, MTL-algebras, etc.) have been studied. Consequently many names have been proposed for these types of filters: Boolean filters, Heyting filters, implicative filters, positive implicative filters, fantastic filters, easy filters, etc. This multiplicity of names for the filters makes it very difficult to study them and the connections between them. To avoid this inconvenience, in this paper we propose a new approach for the study of these filters in residuated lattices, in order to be easily accessible to the readers. We also present a unified treatment of some particular results about filters in residuated lattices ( Theorem 16, Corollary 17).