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Some types of filters in non-commutative residuated lattices

Mahmood Bakhshi


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.


residuated lattices, fantastic filter.

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