<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we introduce a new class of residuated lattice: residuated lattice with (<italic>C</italic>∧&amp;→) property and we prove that (<italic>C</italic>∧&amp;→) ⇔ (<italic>C</italic>→) + (<italic>C</italic>∧).Also, we introduce and characterize <italic>C</italic>→, <italic>C</italic>∨, <italic>C</italic>∧ and <italic>C</italic>∧ &amp; → 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 <italic>C</italic>→ (<italic>C</italic>∨ or <italic>C</italic>∧ or <italic>C</italic>∧&amp;→ 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 <italic>C</italic>∧&amp;→ filters the decomposition conditions.</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.

Some decompositions of filters in residuated lattices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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{"article-title":"Some decompositions of filters in residuated lattices"}

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...

Some decompositions of filters in residuated lattices

Published Online: Mar 02, 2019

Page range: 211 - 231

Received: Jan 30, 2018

DOI: https://doi.org/10.2478/auom-2019-0011

Keywords
Residuated lattice, divisible residuated lattice, BL algebra, MTL algebra, filter, deductive system, filter, filter, filter, filter, MTL filter, divisible filter, BL filter

© 2019 Dana Piciu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Some decompositions of filters in residuated lattices

Published Online: Mar 02, 2019

Page range: 211 - 231

Received: Jan 30, 2018

DOI: https://doi.org/10.2478/auom-2019-0011

KeywordsResiduated lattice, divisible residuated lattice, BL algebra, MTL algebra, filter, deductive system, filter, filter, filter, filter, MTL filter, divisible filter, BL filter

© 2019 Dana Piciu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Residuated lattice, divisible residuated lattice, BL algebra, MTL algebra, filter, deductive system, filter, filter, filter, filter, MTL filter, divisible filter, BL filter