Some decompositions of filters in residuated lattices

Piciu Dana; Dan Christina Theresia; Chirteş Florentina

doi:10.2478/auom-2019-0011

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (Mar 2019)

Some decompositions of filters in residuated lattices

Piciu Dana,
Dan Christina Theresia,
Chirteş Florentina

Affiliations

Piciu Dana: Department of Mathematics, University of Craiova, Al.I. Cuza Street, 13, 200585, Craiova, Romania
Dan Christina Theresia: Department of Mathematics, University of Craiova, Al.I. Cuza Street, 13, 200585, Craiova, Romania
Chirteş Florentina: Department of Mathematics, University of Craiova, Al.I. Cuza Street, 13, 200585, Craiova, Romania

DOI: https://doi.org/10.2478/auom-2019-0011
Journal volume & issue: Vol. 27, no. 1
pp. 211 – 231

Abstract

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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.

Published in Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica

ISSN: 1224-1784 (Print); 1844-0835 (Online)
Publisher: Sciendo
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://sciendo.com/journal/AUOM

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