Abstract
The notion of extended filter of a filter associated to a subset of Rl-monoids is defined and related properties are investigated. Rachunek and Salounova proved that positive implicative filters and Boolean filters in Rl-monoids coincide with a condition in Rachunek and Salounova (Acta Univ Palacki Olomuc Fac rer nat Math 48(1):93---107, 2009). In this paper, we prove that positive implicative filters and Boolean filters coincide without any condition and get some results on various types of filters.
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