Distributive and Dual Distributive Elements in Hyperlattices

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 ∨-semi hyperlattice, respectively. We use the properties of prime ideals and prime filters in hyperlattices. We will proceed to introduce th...

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Veröffentlicht in:Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică 2017-01, Vol.25 (3), p.25-36
Hauptverfasser: Ameri, Reza, Amiri-Bideshki, M., Hoskova-Mayerova, Sarka, Saeid, A. B.
Format: Artikel
Sprache:eng
Schlagworte:
15A60
Distributive element
Dual distributive element
Homomorphism
Hyperlattice
Primary 15A24
Prime filter
Prime ideal
Secondary 65F10
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Beschreibung
Zusammenfassung: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.
ISSN:1844-0835
1224-1784
1844-0835
DOI:10.1515/auom-2017-0032