<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : <italic>Gődel filters.</italic> So, we characterize the filters for which the quotient algebra that is constructed via these filters is a <italic>Gődel algebra</italic> and we establish the connections between these filters and other types of filters. Using Gődel filters we characterize the residuated lattices which are Gődel algebras. Also, we prove that a residuated lattice is a Gődel algebra (divisible residuated lattice, MTL algebra, BL algebra) if and only if every filter is a Gődel filter (divisible filter, MTL filter, BL filter). Finally, we present some results about injective Gődel algebras showing that complete Boolean algebras are injective objects in the category of Gődel algebras.</p></abstract>

In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the quotient algebra that is constructed via these filters is a Gődel algebra and we establish the connections between these filters and other types of filters. Using Gődel filters we characterize the residuated lattices which are Gődel algebras. Also, we prove that a residuated lattice is a Gődel algebra (divisible residuated lattice, MTL algebra, BL algebra) if and only if every filter is a Gődel filter (divisible filter, MTL filter, BL filter). Finally, we present some results about injective Gődel algebras showing that complete Boolean algebras are injective objects in the category of Gődel algebras.

Gődel filters in residuated lattices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Gődel filters in residuated lattices"}

In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the...

Gődel filters in residuated lattices

Publié en ligne: 13 avr. 2021

Pages: 183 - 200

Reçu: 15 janv. 2020

Accepté: 13 mars 2020

DOI: https://doi.org/10.2478/auom-2021-0012

Mots clés
Residuated lattice, Gődel algebra, Gődel filter, injective object

© 2021 Dana Piciu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Gődel filters in residuated lattices

Publié en ligne: 13 avr. 2021

Pages: 183 - 200

Reçu: 15 janv. 2020

Accepté: 13 mars 2020

DOI: https://doi.org/10.2478/auom-2021-0012

Mots clésResiduated lattice, Gődel algebra, Gődel filter, injective object

© 2021 Dana Piciu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Residuated lattice, Gődel algebra, Gődel filter, injective object