In this work, we consider a mimetic definition of maximality for fuzzy filters of lattices, and look for some characterization of this definition. We find out that maximality can be handled by very few elementary properties of fuzzy filters.
Residuated lattices play an important role in the study of fuzzy logic based ont-norms. In this paper, we introduce some notions ofn-fold filters in residuated lattices, study the relations among them, and compare them with prime, maximal and primary, filters. This work generalizes existing results in BL-algebras and residuated lattices, most notably the works of Lele et al., Motamed et al., Haveski et al., Borzooei et al., Van Gasse et al., Kondo et al., Turunen et al., and Borumand Saeid et al., we draw diagrams summarizing the relations between different types ofn-fold filters andn-fold residuated lattices.
The famous Baker-Pixley theorem says that for a finite algebra [Formula: see text] with a majority term operation, an operation f : An → A, n ≥ 1, is a term operation of [Formula: see text] iff f preserves all subuniverses of [Formula: see text]. The aim of this paper is the generalization of this result by replacing [Formula: see text] by an arbitrary congruence on [Formula: see text]. In this way we generalize the concept of primality to θ-primality. Moreover, we introduce the concept of a θ-variety and prove a structure theorem for those classes of algebras.
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