<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

Published Online: Mar 31, 2018

Page range: 25 - 36

Received: Jul 01, 2016

Accepted: Nov 22, 2016

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

Keywords
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

Published Online: Mar 31, 2018

Page range: 25 - 36

Received: Jul 01, 2016

Accepted: Nov 22, 2016

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

KeywordsHyperlattice, 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.

Keywords
Hyperlattice, Prime ideal, Prime filter, Distributive element, Dual distributive element, Homomorphism