Transitivity of ρR relations in hyperrings using geometric spaces

In this paper, we determine a family U R of subsets of a hyperring R and sufficient conditions, such that the geometric space ( R , U R ) is strongly transitive. Finally, we prove that in any hyperfield or any hyperring ( R , + , · ) , such that ( R , + ) has an identity element, ρ R = ρ R ∗ .

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Bibliographic Details
Published in:Boletín de la Sociedad Matemática Mexicana 2018-10, Vol.24 (2), p.359-372
Main Authors: Shirvani, M., Mirvakili, S.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Article
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Description
Summary:In this paper, we determine a family U R of subsets of a hyperring R and sufficient conditions, such that the geometric space ( R , U R ) is strongly transitive. Finally, we prove that in any hyperfield or any hyperring ( R , + , · ) , such that ( R , + ) has an identity element, ρ R = ρ R ∗ .
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-017-0162-x