<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation <italic>θ</italic> on a dual skew HADL <italic>L</italic> and prove that <italic>θ</italic> is a congruence relation on the equivalence class [<italic>x</italic>]<italic>θ</italic> so that each congruence class is a maximal rectangular subalgebra and the quotient [<italic>y</italic>]<italic>θ/θ</italic> is a maximal lattice image of [<italic>x</italic>]<italic>θ</italic> for any <italic>y ∈</italic> [<italic>x</italic>]<italic>θ</italic>. Moreover, we show that if the set <italic>PI</italic> (<italic>L</italic>) of all the principal ideals of an ADL <italic>L</italic> with 0 is a dual skew Heyting algebra then <italic>L</italic> becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.</p></abstract>

In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.

Dual skew Heyting almost distributive lattices

Applied Mathematics and Nonlinear Sciences

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

{"article-title":"Dual skew Heyting almost distributive lattices"}

In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We...

Dual skew Heyting almost distributive lattices

Publié en ligne: 25 juin 2019

Pages: 151 - 162

Reçu: 11 mars 2019

Accepté: 17 avr. 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00015

Mots clés
almost distributive lattice (ADL), maximal element, Heyting almost distributive lattice(HADL), Heyting algebra, skew lattice, skew Heyting algebra and skew Heyting almost distributive lattice(skew HADL)

© 2019 B. Assaye et al., published by Sciendo

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

Dual skew Heyting almost distributive lattices

Publié en ligne: 25 juin 2019

Pages: 151 - 162

Reçu: 11 mars 2019

Accepté: 17 avr. 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00015

Mots clésalmost distributive lattice (ADL), maximal element, Heyting almost distributive lattice(HADL), Heyting algebra, skew lattice, skew Heyting algebra and skew Heyting almost distributive lattice(skew HADL)

© 2019 B. Assaye et al., published by Sciendo

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

Mots clés
almost distributive lattice (ADL), maximal element, Heyting almost distributive lattice(HADL), Heyting algebra, skew lattice, skew Heyting algebra and skew Heyting almost distributive lattice(skew HADL)