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Abstract
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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.
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