<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and ∨-semi hyperlattice, respectively. We use the properties of prime ideals and prime filters in hyperlattices. We will proceed to introduce the notion of dual distributive hyperlattices, I-filters and filters generated by dual distributive elements. Finally, the relationship between good homomorphisms and istributive (resp. dual distributive)elements in hyperlattices are investigated. </p></abstract>

In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and ∨-semi hyperlattice, respectively. We use the properties of prime ideals and prime filters in hyperlattices. We will proceed to introduce the notion of dual distributive hyperlattices, I-filters and filters generated by dual distributive elements. Finally, the relationship between good homomorphisms and istributive (resp. dual distributive)elements in hyperlattices are investigated.

Distributive and Dual Distributive Elements in Hyperlattices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Distributive and Dual Distributive Elements in Hyperlattices"}

In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and...

Distributive and Dual Distributive Elements in Hyperlattices

Publié en ligne: 31 mars 2018

Pages: 25 - 36

Reçu: 01 juil. 2016

Accepté: 22 nov. 2016

DOI: https://doi.org/10.1515/auom-2017-0032

Mots clés
Hyperlattice, Prime ideal, Prime filter, Distributive element, Dual distributive element, Homomorphism

© 2018

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

Distributive and Dual Distributive Elements in Hyperlattices

Publié en ligne: 31 mars 2018

Pages: 25 - 36

Reçu: 01 juil. 2016

Accepté: 22 nov. 2016

DOI: https://doi.org/10.1515/auom-2017-0032

Mots clésHyperlattice, Prime ideal, Prime filter, Distributive element, Dual distributive element, Homomorphism

© 2018

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

Mots clés
Hyperlattice, Prime ideal, Prime filter, Distributive element, Dual distributive element, Homomorphism