A short note on t-filters, I-filters and extended filters on residuated lattices

The notion of a t-filter on residuated lattices was introduced in order to generalize a big amount of particular results about special types of filters (e.g. implicative, positive implicative, fantastic etc.). In this short note we are going to point out the relationship between t-filters and I-filters and also between t-filters and extended filters on residuated lattices.