Some types of filters in non-commutative residuated lattices
In this paper, the concepts of fantastic filter, involution filter and pseudocomplementation filter are introduced and some of their properties and related results are obtained. As a connection with well-known filters; Boolean filters and positive implicative filters, it is proved that a filter is Boolean if and only if it is a fantastic filter and a positive implicative filter. Particularly, it is proved that in an involutive residuated lattice, the concepts of Boolean filter, involution filter and pseudocomplementation filter are coincide.
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