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Boletín de la Sociedad Matemática Mexicana

, Volume 24, Issue 2, pp 359–372 | Cite as

Transitivity of \(\rho _\mathfrak {R}\) relations in hyperrings using geometric spaces

  • M. Shirvani
  • S. Mirvakili
Original Article
  • 46 Downloads

Abstract

In this paper, we determine a family \({\mathfrak {U}}_{\mathfrak {R}}\) of subsets of a hyperring R and sufficient conditions, such that the geometric space \((R,{\mathfrak {U}}_{\mathfrak {R}})\) is strongly transitive. Finally, we prove that in any hyperfield or any hyperring \((R,+,\cdot )\), such that \((R,+)\) has an identity element, \(\rho _\mathfrak {R}=\rho ^*_\mathfrak {R}\).

Keywords

Hyperring Strongly transitive geometric space Equivalence relation 

Mathematics Subject Classification

20N20 16Y99 

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Copyright information

© Sociedad Matemática Mexicana 2017

Authors and Affiliations

  1. 1.Department of MathematicsPayame Noor UniversityTehranIran

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