Obstinate, weak implicative and fantastic filters of non commutative residuated lattices

In this paper, we introduce the notions of obstinate filters, weak implicative filters and fantastic filters on a non commutative residuated lattice and study their properties. Some characterizations of these filters are obtained. The relations among these filters and (sub) positive implicative filters are investigated. It is proved that each obstinate filters are sub positive implicative filters but the converse may not be true. Then the conditions under which a sub positive implicative filter is an obstinate filter are obtained. Also, we prove that each sub positive implicative filters are (fantastic) weak implicative filters and the converse may not be true. We establish the condition under which a (fantastic) weak implicative filter is a sub positive implicative filter. © 2016, African Mathematical Union and Springer-Verlag Berlin Heidelberg.