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Heyting, Boolean and Pseudo-MV Filters in Residuated Lattices
Saeed Rasouli

The paper is devoted to introduce the notions of left-(right-)Heyting, left-(right-)Boolean and left-(right-)MV filter in residuated lattices and to investigate their properties. Several characterizations of these notions are derived. We show that each left-(right-)Heyting filter is left-(right-)normal and each left- and right-Heyting filter is a Heyting filter. The relations between left-(right-)Boolean filters and left-(right-)Heyting filters are investigated and we prove that left-(right-)Boolean filters are left-(right-)Heyting and this implication is strict. The conditions under which a left-(right-)Heyting filter is left-(right-)Boolean are established. Finally, we show that a filter is Boolean if and only if it is Heyting and pseudo-MV.

2010 Mathematics Subject Classification: 06F99,06D20

Keywords: Residuated lattice, Heyting algebra, Boolean algebra, implicative filter, positive implicative filter, fantastic filter, Heyting filter, Boolean filter, MV filter.

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