Saeed Rasoli

This paper is devoted to introduce the notions of n-fold left-(right-)Heyting, n-fold left-(right-)Boolean and n-fold left-(right-)MV filters in residuated lattices and to investigate their properties. Several characterizations of these notions are derived. The relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)Heyting filters are investigated and we prove that an n-fold left-(right-)Boolean filter is an n-fold left-(right-)Heyting filter, respectively, and this implication is strict. Also, the relations between n-fold left-(right-) Boolean filters and n-fold left-(right-)MV filters are investigated and we show that a normal n-fold left-(right-)Boolean filter is a normal n-fold left-(right-)MV filter and each n-fold left-(right-)Heyting and n-fold left-(right-)MV filter is an n-fold left-(right-)Boolean filter.