Some decompositions of filters in residuated lattices

Piciu, Dana; Dan, Christina Theresia; Chirteş, Florentina

doi:10.2478/auom-2019-0011

Abstract

In this paper we introduce a new class of residuated lattice: residuated lattice with (C∧_&→) property and we prove that (C∧_&→) ⇔ (C_→) + (C∧).Also, we introduce and characterize C_→, C∨, C∧ and C∧ _{& →} filters in residuated lattices (i.e., we characterize the filters for which the quotient algebra that is constructed via these filters is a residuated lattice with C_→ (C∨ or C∧ or C∧_&→ property). We state and prove some results which establish the relationships between these filters and other filters of residuated lattices: BL filters, MTL filters, divisible filters and, by some examples, we show that these filters are different. Starting from the results of algebras, we present for MTL filters, BL filters and C∧_&→ filters the decomposition conditions.

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Some decompositions of filters in residuated lattices

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